227, 228, 230, 238, 239, 241].

  3. 3.

Transformation coefficients as signal representations: In these approaches,
the generated mappings are treated as transformed representations of the
signal. Subsequently, these representations are subjected to further signal-
processing techniques to extract features of interest, such as entropy,
energy, and statistical properties [209, 210, 213, 214, 215, 234, 235, 236,
237, 224, 225, 226, 218, 221, 229]. Compared to the other two approaches,
these methods generally result in a smaller number of features, making them
more suitable for applications with low computational requirements.

Spectral kurtosis (SK) [242, 243] is a popular time-frequency analysis tool in
signal processing that is commonly used to locate harmonics, transients, and
repetitive impulses in the frequency domain. SK is based on computing the
normalized fourth-order moment (kurtosis) of the STFT of the signal at each
frequency bin, providing a statistical measure of the signal’s characteristics
at each time-frequency instant. Essentially, SK quantifies the ”peakedness” or
impulsiveness of the distribution of the power at each frequency bin. One of
its primary applications is the detection of transient components in signals.
Transients, due to their short and sharp nature, create distinct, non-Gaussian
patterns in the signal’s frequency content. When these features are present,
the kurtosis values in the affected frequency bins will be significantly
higher than those of normal behavior. Accordingly, high SK values can indicate
the presence of impulses or bursts, as they cause a deviation from the
Gaussian distribution typically observed in stable operating conditions. This
is particularly useful in condition monitoring and fault diagnosis of rotating
machinery and mechanical systems [244, 245, 246], where transient vibrations
often indicate faults. Additionally, SK is an effective tool for
distinguishing between harmonic components— which often manifest as
consistent, periodic components— and noise in the signal. These harmonics will
often show higher kurtosis values, indicating a non-Gaussian distribution,
possibly due to the periodic and repetitive nature of the harmonics. In
contrast, Gaussian noise tends to have a kurtosis value close to 0, indicating
a Gaussian distribution.

###  V-C Signal Decomposition-Based Methods

Signals generated by physical systems typically consist of multiple components
or modes of time-varying nature in amplitude, phase, and frequency. These
components contain meaningful information about the underlying structure of
the signal. Decomposition techniques attempt to decompose the signal into
elementary modes, enabling signal analysis at the level of its constituent
components. This, in turn, allows for the extraction of highly distinctive
features, that are closely related to the inherent structure of the signal.
Common decomposition approaches include wavelet-based decomposition and
adaptive mode decomposition (ADM) methods. In wavelet-base decomposition
methods [44, 240, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258,
259, 260, 261, 262, 263, 264, 265, 266, 267], discrete wavelet transform
(DWT), stationary wavelet transform (SWT), and wavelet packet transform (WPT)
are commonly used to decompose the signal into elementary modes of high and
low-frequency components using digital filter banks. The performance of
wavelet decomposition is highly dependent on the base wavelet function and the
level of decomposition. AMD methods [268, 249, 254, 269, 270, 271, 272, 273,
274, 275, 276, 277, 278, 279, 280, 281, 282, 283] utilize an empirical
decomposition approach where the signal is adaptively decomposed into a set of
simpler functions known as intrinsic mode functions (IMFs). Hence, in contrast
to wavelet-based methods, AMD methods use an adaptive mechanism rather than a
priori basis function to decompose the signal, leading to more ’natural” modes
that are not influenced by a priori basis function [47]. Moreover, the ability
of AMD methods to adapt to varying signal characteristics makes them effective
when dealing with nonlinear and nonstationary signals. However, this
adaptability comes at the cost of higher computational complexity.
Furthermore, AMD methods are generally sensitive to noise because they rely on
the extrema and minima of the signal for signal decomposition. Additionally,
they suffer from inherent limitations, such as end effect [48] and mode mixing
[49]. Various methods have been introduced to address these limitations, such
as ensemble empirical mode decomposition (EEMD) [50] and variational mode
decomposition (VMD)[51], local mean decomposition [52], and empirical wavelet
transform (EWT) [53].

In the existing literature, signal decomposition is utilized through two
approaches for feature extraction; each approach serves a distinct objective:

  1. 1.

Extraction of highly discriminative features: In these methods, features are
extracted from elementary modes resulting from the decomposition process.
Accordingly, feature extraction methods can be generally grouped under four
main categories: entropy-based [262, 263, 267, 273, 274, 283], energy-based
[251, 257, 264, 265], spectral-based [44, 252, 266, 272, 275, 280, 282, 283],
and statistical-based [247, 250, 249, 251, 253, 254, 260, 261, 275, 283].
Entropy as a measure of uncertainty, is used to quantify the irregularity
within the decomposed modes. Energy-based approaches utilize the changes in
energy content of the decomposed modes to extract the features. Spectral-based
approaches use spectral characteristics of the elementary modes to extract the
features. Statistical-based approaches rely on time-domain properties of the
modes such as skewness, kurtosis, Root-Mean-Square (RMS), and crest factor for
feature extraction.

  2. 2.

Obtaining a low-redundancy (highly informative) version of the composite
signal [240, 268, 248, 255, 256, 258, 259, 269, 270, 271, 276, 277, 278, 279,
281]: This is accomplished by decomposing the signal into elementary modes and
applying further processing to examine these modes based on predefined ranking
criteria. The highest-ranked mode is thus selected and various feature
extraction techniques can be applied to the selected mode accordingly. Here,
the selected mode represents a low-redundancy and high-informativeness version
of the original signal.

An important aspect of the first approach is that it provides a convenient way
to construct a feature vector of controllable size and highly discriminative
nature [44], which is particularly helpful in applications with limited
computational resources. This is facilitated by decomposing the signal into a
finite number of modes and extracting a few features from each mode. For
instance, decomposing the input segment of a signal into $8$ modes and taking
the energy or entropy of each mode as a feature leads to a feature vector with
a size of $1\times 8$ distinctive features. It is also less computationally
intensive than the second approach, making it more suitable for real-time
processing and applications with limited processing capabilities. However, by
focusing on the highest-ranked mode, the second method ensures that the
extracted features are highly informative and less redundant. Moreover, the
capability to rank and select modes based on predefined criteria allows for
dynamic screening that can be automatically adapted according to the nature of
the input signal, which becomes particularly useful in applications that
involve multiple signals from various sources, such as advanced diagnostic
systems and integrated condition monitoring applications. Additionally,
selecting the most informative mode can result in more accurate and relevant
feature extraction, potentially improving the performance.

###  V-D Envelope-Based Methods

Envelope-based feature extraction methods [284, 285, 286, 287, 288, 289, 290,
291, 292, 293, 294, 295] primarily focus on analyzing the envelope of the
signal to reveal essential characteristics of its amplitude, such as
statistical properties, peak frequency, energy, and entropy. In these methods,
The HT is commonly used to obtain the signal’s envelope, which is then
subjected to various feature extraction techniques. Envelope-based feature
extraction is particularly useful in applications where amplitude modulation
(AM) is a key characteristic of the signal; that’s it, the amplitude of the
signal is varied or altered in response to specific factors that are of
interest, for instance, impacts generated by defects in rolling bearings
[296]; in such situations, envelope-based analysis can effectively extract
meaningful features. Generally speaking, as an amplitude-focused approach,
envelope analysis offers limited frequency information about the signal.
Furthermore, its effectiveness can vary significantly depending on the nature
of the signal, as not all signal types are amenable to envelope-based
analysis. Additionally, it is highly susceptible to noise that contaminates
the signal’s amplitude such as impulsive noise, making it difficult to extract
effective features from the envelope [295].

The selection of an appropriate feature extraction method for a given signal
depends on several factors, including the nature of the signal, the specific
requirements of the application, and the available computational resources.
For stationary signals, where the primary interest lies in frequency analysis,
Fourier analysis provides a highly efficient approach to identifying dominant
frequency components within the signal. In scenarios involving comparative
spectral analysis of multiple signals that vary in length and/or bandwidth,
PSD is particularly advantageous since it provides a normalized spectral
density measure, facilitating effective comparison. On the other hand, signals
exhibiting time-varying spectral characteristics necessitate the use of proper
time-frequency analysis for effective feature extraction. The STFT offers a
computationally efficient tool for time-frequency analysis of the signal.
However, its fixed resolution across all frequencies reduces its effectiveness
for applications requiring variable-resolution analysis. In such contexts,
wavelet analysis presents a practical solution due to its ability to perform
multi-resolution analysis through scaled and shifted versions of a wavelet
base function. For analyzing nonstationary and nonlinear signals characterized
by rapidly changing components, the HHT provides an adaptive and more robust
approach than Wavelet analysis but with more computational requirements. The
WVD provides a practical approach for achieving a joint energy-time-frequency
representation of the signal, although it is computationally intensive
compared to the other transforms. It is particularly useful in high-resolution
analysis scenarios or where energy concentration is a focal requirement.
Signal decomposition techniques enable signal analysis at the level of its
constituent components. This, in turn, allows for the extraction of highly
distinctive features of a controllable size that are closely associated with
the inherent structure of the signal. The envelope-based analysis is
especially effective in applications where the envelope characteristics are of
primary interest.

##  VI Challenges and Potential Solutions

The practical deployment of signal-based ML systems faces significant
challenges that can impede the efficiency and effectiveness of the system. Key
among these challenges are the detrimental effects of noisy environments on
signal integrity, the limited availability of abnormal samples, and
computational complexity. These challenges require effective solutions to
mitigate their effects and enhance signal processing techniques. This section
delves into each of these challenges, exploring their implications and
highlighting potential solutions.

###  VI-A Effects of Noise

In real-world systems, signals are nonstationary, nonlinear in nature, and
subject to noise [297]. From a measurement perspective, noise can be defined
as any unwanted signal present in the measurement process other than the
desired signal [298]. In signal processing, noise generally refers to any
unwanted or random variation in the signal that can obscure or distort the
intended information. It is an inevitable part of signal processing,
particularly in machine learning applications where it can hinder feature
extraction and significantly reduce its discriminative power.

####  VI-A1 Noise characteristics

Noise, originating from various sources that are typically present in all
measurement environments can be grouped into three main categories [298]:

  1. 1.

Intrinsic noise that arises from random fluctuations within measurement
physical systems such as thermal and shot noise.

  2. 2.

Man-made noise sources such as motors, power lines, radio broadcasts,
oscillators, laboratory equipment, and cellular phones.

  3. 3.

Noise caused by natural disturbances such as lightning and sunspots.

Understanding the characteristics of noise and how it affects the desired
signal is the first step toward an effective noise removal approach. Noise is
typically modeled and characterized by various aspects such as spectrum, mode
of occurrence, and statistical distribution.
Noise Spectrum (Noise Colors): Color of noise is a spectral-based description
of noise where different “colors” of noise are classified according to their
power spectral densities. The most important and common type in the context of
signal processing is white noise. A defining characteristic of this type of
noise is its flat power spectral density (PSD). Thus, it has a constant power
at each frequency, affecting all frequencies in the desired signal equally.
Pink noise, or $\frac{1}{f}$ noise, has a PSD that decreases proportionally to
the inverse of its frequency, making it more dominant at lower frequencies in
the desired signal. In contrast, blue noise mainly impacts high-frequency
comments in the signal since its PSD increases proportionally to the
frequency. Purple noise has more energy at higher frequencies compared to blue
noise since its PSD increases with frequency at a much faster rate than that
of blue noise.
Occurrence Nature: The presence of noise in the signal depends on the nature
of the occurrence of noise. Continuous noise is present continuously during
signal acquisition, persistently contaminating the signal over its entire
duration. The severity of continuous noise is characterized by its amplitude
(power); it is related to the signal power by the signal-to-noise ratio (SNR),
which provides a measure to evaluate the severity of the noise and the
performance of the signal denoising technique employed. Intermittent noise, in
contrast, occurs at irregular intervals. Burst noise, on the other hand, is
characterized by sudden occurrences, often of short durations. Impulse noise
consists of random noise pulses. Compared to burst noise, impulse noise has
extremely short durations. Burst and impulse noises are characterized by their
large amplitudes compared to the desired signal.
Statistical Distribution: Noise can be described in terms of amplitude
distribution. Gaussian noise, commonly called additive white Gaussian noise
(AWGN), is a common noise model in signal processing. Characterized by its
Gaussian distribution, the amplitude of AWGN can be completely described by
its mean and variance, which represent noise power. AWGN is commonly modeled
as a zero-mean Gaussian process, maintaining the mean of the desired signal
unchanged. As a white continuous noise, AWGN affects the spectral contents of
the signal equally.

####  VI-A2 Signal Denoising Techniques

As mentioned earlier, the process of signal denoising involves eliminating
noise while preserving the important features of the signal. The first step in
signal processing-ML pipelines is to remove noise and outliers. Thus, the
effectiveness of subsequent steps depends heavily on the efficiency of the
employed signal denoising technique. For impulse and burst noise, Order-
Statistic Filtering (OSF) [299] is particularly effective; it is based on
replacing each sample in the signal with a statistic (like the median,
minimum, or maximum) calculated from the samples in its neighborhood, defined
by a sliding window of a certain size that moves across the signal. The median
filter [300, 301, 302, 303], a specific type of OSF, is widely used to remove
impulsive noise. OSF is highly robust to outliers such as impulse noise since
order statistics are less sensitive to extreme values than linear operations
such as averaging. Moreover, the median filter is highly effective in
preserving signal edges (sudden changes in signal amplitude) while reducing
noise, which is crucial for maintaining the integrity of the signal’s
features. The efficiency of the median filter is significantly influenced by
the selection of the window size. A larger window size will include more
samples, improving the ability to remove impulsive noise. However, a larger
window could over-smooth the signal, potentially erasing important details.
Further, it will increase the computational burden. Conversely, a smaller
window size preserves more detail since fewer samples are involved in
determining the median, but it may be less effective in removing noise as the
median value will be influenced by the presence of noise in the window.
Additionally, the performance of median filters is limited by the proportion
of impulsive noise in the window. Filtering performance decreases as the
proportion of impulsive noise increases [304]. Specifically, with low levels
of impulsive noise, the noise spikes are likely to be the minority within the
window, and the median value computed within the window is likely to be a true
signal value, effectively removing the noise. As the proportion of impulsive
noise increases, there’s a higher likelihood that the median value computed
within the window will itself be a noise value, especially if the noise spikes
constitute a considerable part of the samples in the window. In this case,
replacing the original signal sample with the median does not remove the
noise. Instead, it might even introduce additional distortion, especially if
the median value is a noise spike. To overcome these problems, adaptive median
filtering is commonly applied where the window size changes adaptively based
on impulsive noise content [304, 305, 306].

For complex noise patterns such as intermittent and continuous noise, several
techniques can be used to denoise the signal in the time domain, frequency
domain, time-frequency domain, or deep learning (DL) latent space. Time-domain
methods involve techniques that directly manipulate the signal in the time
domain, aiming to identify and reduce noise components while preserving signal
characteristics. Moving average (MA) filter [307, 308] is a simple yet
effective method that smooths the signal by averaging neighboring data points.
It is particularly useful for reducing simple random noise while preserving
the signal’s shape. Traditional MA filters operate by averaging a set of
signal data points (referred to as the window or kernel) and sliding this
window across the signal. This process smooths out short-term fluctuations,
effectively reducing random noise. However, the primary limitation of a
traditional moving average filter is its fixed window size, which may not be
optimal for all signal conditions. Adaptive moving average (AMA) filters [309,
310, 311] address this limitation by dynamically adjusting the window size
based on the characteristics of the input signal. Here, the window size
changes in response to the variability or other statistical properties of the
signal. This adaptivity is critical when dealing with nonstationary signals or
when the noise characteristics are inconsistent throughout the signal. The
design of the adaptive mechanism involves selecting proper criteria for window
size adjustment. Common approaches include the use of local signal variance,
rate of change, or other statistical measures that reflect the signal’s
nature.

The Savitzky-Golay filter (SGF) [312, 313, 314] While it shares some
conceptual similarities with MA filters, it provides a different approach to
noise reduction and is particularly useful for preserving higher-order signal
properties. Specifically, MA filters give equal weight to all points in the
window, which can distort the features of the signal. On the other hand, SGF
performs a local polynomial regression on the signal data points present in
the moving window to provide a more nuanced smoothing that preserves the
original shape and characteristics of the signal. This approach not only
smooths the data but also preserves features of the data points, such as
relative maxima, minima, and width, which are often obscured by noise. The
design of an SGF involves the proper selection of the window size, and the
order of the polynomial [72, 73, 74, 75]. The selection depends on the
specific characteristics of the signal being processed and the nature of the
noise. A higher polynomial order can better adapt to changes in the signal’s
trend, but it may also introduce noise if not chosen appropriately.

Adaptive filters leverage adaptive noise cancellation (ANC) techniques to
instantly isolate and remove unwanted noise from the signal, making them
suitable for real-time applications such as autonomous driving, navigation,
control systems, and robotics. ANC involves dynamically adjusting the filter
parameters to minimize the difference between the desired signal (primary
signal of interest) and the actual signal; the primary goal is to improve the
SNR without distorting the primary signal. Common ANC techniques involve the
least mean square (LMS) and recursive least square (RLS) adaptive filters
[315, 316, 317, 318], and Kalman filtering (KF) [319, 320, 321, 322]. LMS
adaptive filtering, a gradient-based method, attempts to minimize the mean
square error between the desired and actual output of the filter. To
facilitate the generation of an estimate of the unwanted noise, this process
entails using a reference signal, highly correlated with the noise
contaminating the primary signal and uncorrelated with the primary signal
itself. The RLS algorithm provides a recursive solution to the least-squares
problem, offering faster convergence than LMS. In contrast to LMS and RLM,
which require a prior reference signal, KF estimates the state of the system,
represented by the signal of interest, based on noisy measurements. The
estimation is based on Bayesian estimation and state-space representation of
linear systems [323], making KF particularly useful in real-time applications
involving time-varying signals or systems with inherent uncertainties. KF
consists of two main steps: prediction and update. In the prediction phase, KF
predicts the next state of the system. In the update phase, the prediction is
adjusted using the new measurement data, refining the system’s state estimate.
In the context of noise reduction, this process inherently filters out the
noise from the measurements, isolating the primary signal. Standard KF assumes
that noise is Gaussian and the system has linear dynamics. However, several
extensions have been developed to handle more complex scenarios. Such as the
extended Kalman filter (EKF) and the unscented Kalman filter (UKF) [324].
However, the design of KF requires a good understanding of system dynamics and
noise characteristics.

Singular spectrum analysis (SSA), which is a well-known method to decompose
time series into trends, seasonal components, and noise, has been explored
within the signal processing field for signal denoising applications [325,
326, 327, 328, 329, 330, 331] due to its effectiveness in separating useful
oscillatory components from noisy signals. SSA works by embedding a signal in
multidimensional space, constructing a trajectory matrix by sliding a window
over the signal data points. The trajectory matrix is then decomposed using
Singular Value Decomposition (SVD), which separates the signal into a series
of matrices associated with singular values. These matrices represent
different signal components, including deterministic structures and stochastic
noise. Accordingly, the decomposed components are classified into groups that
represent the signal and noise, respectively. This involves evaluating
singular values and the corresponding eigenvectors to differentiate between
signal information and noise components. The denoised signal is then
reconstructed by summing the respective groups of matrices that contain signal
information. Subsequently, the reconstructed components are transformed back
into the time domain. The effective implementation of SSA in the context of
signal denoising involves two main aspects: Selecting an appropriate window
length and accurately grouping singular values and eigenvectors corresponding
to signal information and noise components. These aspects are pivotal as they
directly influence the quality and reliability of the signal-denoising
process. The choice of window length determines the structure of the
trajectory matrix and subsequently affects the decomposition and
reconstruction phases. An appropriately chosen length ensures that the
resulting trajectory matrix captures the underlying structure of the signal,
effectively separating signal components and noise. A window length that is
extremely short may not capture the signal’s dynamics adequately, while a
window length that is too long may reduce denoising efficiency and increase
computational complexity. However, selecting an optimal length is not
straightforward; it is highly dependent on the specific characteristics of the
signal, including periodicity and stationarity [326]. In practice, selecting
an appropriate window length depends on prior knowledge of signals of interest
and often ultimately relies on experimentation [327, 330] where empirical or
heuristic methods are often employed to determine a suitable window length for
a specific application. Additionally, the accurate grouping of decomposed
components is fundamental for effective signal denoising as misclassification
of these components can lead to either an inadequate removal of noise or the
unintended discarding of useful signal information. There is no general rule
for the grouping process; it is mainly determined by the specific requirements
of the application, the statistical nature of the signal of interest, and
associated noise [330].

Frequency-domain noise reduction is based on the signal’s frequency content,
where noise is often more distinguishable due to its distinct spectral
characteristics. Common frequency-domain techniques involve frequency-
selective filtering and spectral subtraction (SS). Frequency-selective filters
include low-pass [332, 333, 334], high-pass [335, 336, 334], band-pass [337,
338], and notch filters (band-stop) [339, 340]. These filters attenuate noise
components that are outside the primary frequency range. Specifically, low-
pass filters allow components with frequencies lower than their defined cutoff
frequency to pass through while attenuating components with frequencies higher
than the cutoff. Conversely, high-pass filters perform the opposite operation,
blocking frequencies below the cutoff. Band-pass filters pass frequencies
within a certain range and attenuate frequencies outside that range. Notch
filters attenuate specified narrow frequency bands. Frequency-selective
filtering techniques are useful in applications where noisy frequency
characteristics are known, such as noise caused by power-line and equipment
interference. SS [338, 341, 342, 343, 344, 345, 346, 347] relies on estimating
the noise spectrum and subtracting it from the noisy signal’s spectrum. In
contrast to frequency-selective filtering, which eliminates specific
frequencies in the signal spectrum, SS provides global spectrum denoising
mechanisms. The main steps in SS involve estimating the power spectrum of
noise and subtracting it from the power spectrum of the original signal to
obtain a new power spectrum. Negative values are eliminated by setting them to
zero. The new power spectrum is combined with the phase of the original signal
to reconstruct the denoised signal’s time waveform. The noise spectrum is
commonly estimated and updated during signal-inactivity periods where only
noise is present. SS generally has moderate computational complexity [348].
Hence, it offers practical solutions in cases where noise is generally
characterized as a stationary or a slowly varying process independent of the
desired signal. However, in practice, random noise variations can lead to an
overestimation of noise’s power spectrum, leading to many negative values in
the subtracted spectrum. While these values can be eliminated by replacing
them with zeros, this nonlinear rectification process can cause significant
distortion in the recovered signal [348], necessitating the adaptation of
enhancement mechanisms [338, 345] that come at the cost of increased
computational complexity.

Time-frequency denoising methods are commonly applied for nonstationary
signals since their varying spectral contents make traditional time-domain or
frequency-domain methods less effective. The main concept of time-frequency
denoising methods is centered around discriminating and eliminating noise-
related coefficients within the time-frequency domain representations of the
noisy signal. Time-frequency denoising involves transforming the signal into
the time-frequency domain, representing it by a set of coefficients
corresponding to each time-frequency instant. Since each coefficient reflects
the signal’s energy at that instant, signal denoising is achieved by screening
these coefficients to distinguish between noise and meaningful signal
components. Thresholding is a common technique employed in this stage; it
involves setting a threshold value, below which coefficients are considered to
represent noise and are, therefore, attenuated or set to zero. Coefficients
above the threshold, which are assumed to represent the actual signal, are
either preserved or adjusted. The key idea here is that small-magnitude
coefficients. representing low energy, are more likely to be associated with
noise, while larger coefficients are likely to represent actual signal
components. After thresholding, the time-domain signal is reconstructed by
inversely transforming the modified coefficients to the time-domain. Wavelet-
based thresholding [45, 349, 350, 351, 352, 353, 354, 355, 356] is commonly
used for signal denoising, mainly attributed to its unique characteristics of
multi-resolution analysis and the availability of a large set of basic
functions. Multi-resolution analysis can capture global trends and fine
details, making it useful in denoising. The diverse family of wavelet base
functions allows the selection of a wavelet that matches signal
characteristics. In thresholding-based denoising, the noise level is
determined by the threshold value. Hence, excessively large thresholds could
filter out some of the useful signal representations; on the other hand, too
small thresholds could cause some noise to be retained in the signal. There
are several methods to guide the selection of an appropriate threshold, such
as universal threshold, minimax threshold, and SURE threshold [356]. Common
thresholding functions include hard thresholding and soft thresholding [351].
In hard thresholding, coefficients with absolute values less than the
threshold are set to zero, while others remain unchanged. This can sometimes
lead to discontinuities in the reconstructed signal. Soft thresholding, on the
other hand, shrinks coefficients towards zero by the threshold value,
providing a smoother result but potentially introducing bias. The choice of
thresholding function and threshold values is influenced by the
characteristics of the signal and the specific requirements of the application
[356, 357, 350, 358, 359, 360]. In practice, it is an iterative process where
thresholding and signal reconstruction are repeated, and the thresholding is
adjusted at each iteration based on denoising performance.

The use of DL for signal-denoising applications is an active research field
[361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375,
376, 377, 378]; the existing approaches involve a wide range of models and
methods, making them too numerous to mention. Nevertheless, the main theme is
to use noise-free signals as training targets and corresponding noisy versions
as training inputs. From a signal-processing perspective, such an approach can
be centered around the concept of tunable denoising filters, Where a trained
DL denoising model can be viewed as a tuned denoising filter whose
coefficients, represented by model weights, are tuned through the training
phase to remove noise from the signal. DL-based approaches are approved to be
highly effective in noise removal due to their ability to learn complex, noisy
patterns and related dependencies within the signal. Moreover, they can be
designed to implement various operations on signal simultaneously,
facilitating efficient end-to-end implementation of various signal-processing
pipelines. This concept has been demonstrated in [378], where 1D convolutional
autoencoders are utilized to implement a signal processing pipeline that
smooths, compresses, denoises, and expands vibration signals. The pipeline is
intended to facilitate power-efficient remote condition monitoring. The
smoothing and compression operations were implemented simultaneously using a
smoothing autoencoder with a $\mu$-law compression-based activation function.
The simultaneous denoising expansion of the compressed noisy signal is
realised by a denoising reconstruction autoencoder.

Despite these advantages, the effectiveness of DL-based denoising, in general,
is limited to noise profiles that are present in the training set [379].
Furthermore, as they lack inherent capabilities to adapt to varying noise
patterns, conventional DL denoising approaches are impractical for real-time
applications that involve varying noise characteristics.

###  VI-B Availability of Labeled Abnormal Samples

In supervised ML models, labeled samples that are large in size and diverse—in
terms of class representation— should be available to serve the training
purpose. In real-world situations, the available labeled samples are usually
limited in their size due to expensive and time-consuming labeling processes.
Moreover, faulty or abnormal samples are not abundant since abnormal events,
such as faults or anomalies, are infrequent, making it difficult to gather
substantial abnormal signal data. As a result, real-world abnormal samples are
usually insufficient to represent the corresponding classes during the
training phase. There are several solutions in the literature to address this
problem. DL-based solutions are becoming increasingly popular where transfer
learning techniques are commonly adapted to avoid learning from limited
labeled data [380, 381, 382, 383]. These approaches overcome the problem by
adapting pre-trained models to extract deep features from the limited
available signal samples, eliminating the need for model training. Recent
trends utilize few-shot learning (FSL) [384, 385, 386, 387], enabling the pre-
trained models to generalize over new categories of data using only a few
labeled samples per class. While DL-based solutions show promising results,
they are computationally intensive. Additionally, In contrast to computer
vision, where mature pre-trained models can be developed using large-scale and
well-labeled datasets [388], the development of pre-trained time-series models
[389, 390, 391] as generic feature extractors is still an evolving area of
research.

Non-ML solutions [392, 393, 394, 395, 396, 397, 398, 267] employ signal
processing techniques for feature extraction and use similarity-based
classification, providing a computationally efficient alternative to DL-based
solutions. In these methods, features are extracted from available labeled
normal samples, and a ”normality” reference model is constructed from these
features. Accordingly, signal classification is achieved by assessing the
similarity between unknown samples and the reference model in the feature
space. In tasks involving multiple classes, the process entails comparing
unknown samples with reference samples representing different classes. The
class of the unknown sample is then determined to be the class of the
reference sample with the highest similarity score.

Other solutions utilize data augmentation techniques [399, 400, 401] to
generate additional pseudo-samples. This is achieved by applying “label-
invariant” transformations to available signal samples, which can considerably
promote the final classification performance and generalization ability of the
ML model [401]. However, compared to image augmentation [402], which relies
mainly on spatial transformations, signal augmentation involves unique
challenges stemming from the complexity of the temporal and spectral
characteristics of the signal. This complexity would reduce the augmentation
reliability, consequently hindering the generalization of the employed model.
To overcome this challenge, signals can be transformed into 2D time-frequency
imagery representations, such as spectrogram and scalogram, where conventional
image augmentation can be applied accordingly [403, 404, 405]. However,
although 2D time-frequency representations and classical images possess
similar data structures, they fundamentally differ regarding what information
is conveyed along the $x-y$-color space. Thus, employed data augmentation
techniques should correlate with a real-world, physical transformation of the
signal [403]. While this is feasible for signals with well-defined
characteristics, such as sound signals, it becomes impractical for complex
signals.

Advanced approaches leverage the powerful synthesizing capabilities of
generative adversarial networks (GANs) to generate new synthetic samples with
reliable characteristics [406, 407, 408, 409, 410, 411]. The advancement in
computational capabilities enables the feasible implementation of these
approaches despite their intensive computational requirements. Further, as an
offline operation, synthesizing new samples does not impact online inferencing
tasks.

###  VI-C Computational Complexity

Computational complexity is a major concern in the real-world deployment of
signal-based ML systems. The complexity of these systems is twofold: the
complexity associated with signal processing and the complexity inherent in
the used ML model. From a signal processing perspective, the complexity is
mainly attributed to three factors [44]: the size of the signal segment
$N_{o}$, algorithm-based computations involved in preprocessing and feature
extraction, and the size of the resultant feature vector. While the complexity
stemming from algorithmic computations is a fundamental aspect of the chosen
approach, several techniques can be employed to reduce the influence of
segment length and feature size on the complexity.

####  VI-C1 Segment Length

The segment length, represented by the number of samples in the segment, is a
significant factor in signal processing since it directly impacts the
computational complexity, system delay, and reliability of extracted features.
Therefore, selecting a proper segment length is generally a balancing act that
necessitates a thorough consideration of the trade-offs involved. It is often
guided by theoretical analysis, empirical evaluation, and domain-specific
knowledge. Considering oversampled signals, which is the common case in many
applications, decimation can be used to reduce the signal’s sampling rate,
thereby decreasing the number of samples in the segment while maintaining the
same time duration. The decimation process involves two steps: Applying low-
pass filtering to the signal to prevent aliasing. The low-pass filter limits
the signal’s bandwidth to satisfy the Nyquist criterion, ensuring that the
highest frequency in the signal is less than half of the new reduced sampling
rate. Accordingly, the second step involves down-sampling the filter signal by
retaining every $M$th sample and discarding the rest, where $M$ is the
decimation factor. For instance, if $M=4$, the process would keep every fourth
sample and discard the three in between. Decimation is widely utilized in
digital signal processing (DSP) applications [412, 413]. However, the
application of decimation requires a deep understanding of the frequencies of
interest in the signal. To the best of our knowledge, the application of
decimation in the context of feature extraction and, consequently, its
effectiveness remain unexplored.

####  VI-C2 Size of Extracted Features

In contrast to the length of the signal segment, which influences the
complexity of the signal processing pipeline, the dimensionality of the
extracted features primarily affects the complexity of the employed ML model.
There is a wealth of well-established methods in the ML literature that can
effectively decrease feature size, thereby relaxing computational complexity
and reducing feature redundancy. Common methods include dimensionality
reduction [414, 415, 416, 417, 418, 419, 420, 421, 414] and feature ranking
and selection [422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433,
125, 8, 434, 414]. In DL-based feature extraction methods, the substantial
size of the resultant deep-learned features necessitates dimensionality
reduction since these features constitute a multi-dimensional latent space.
Moreover, since these features lack interpretability, feature ranking and
selection become essential to identify the most relevant features. In the
context of signal processing-based features, these techniques are commonly
employed when many features— such as Fourier, wavelet, and energy-time-
frequency coefficients— are used. Despite their effectiveness in reducing the
computational burden and improving the efficiency of the ML model,
dimensionality reduction and feature selection come at the cost of extra
processing, increasing the system’s end-to-end complexity and time delay. An
alternative solution is to utilize various signal processing tools to develop
a small set of highly distinctive features. Although this typically demands
domain knowledge and empirical evaluation, certain signal-processing tools can
be particularly useful in this context. Specifically, Signal decomposition
offers a reliable way to engineer a few highly-discriminative features from
decomposed modes [44] that are closely associated with the inherent structure
of the signal. The size of the features extracted from these modes equals
$1\times(K\times M)$ [44], where $K$ is the number of decomposed modes and $M$
is the number of extracted features for each mode. In [44], this approach was
utilized for vibration-based condition monitoring of rolling bearings using
wavelet-based decomposition. A comparative analysis shows that the approach
would achieve excellent performance in fault detection with very few features
compared to other approaches. Furthermore, the comparison shows that the
decomposition-based method allows for shorter input segments, attributed to
the high localization of the decomposed modes in both time and frequency.

##  VII Applications

This section delves into the practical application of signal-processing
techniques for feature extraction in signal-based ML systems. By providing
actual use cases, the section aims to bridge the theoretical foundations of
signal processing with its tangible use in real-world scenarios. To foster a
collaborative research environment and support reproducibility, the Python
codes related to these use cases are made publicly accessible on the Github
site of the Optimized Computing and Communications (OC2)
Laboratory444https://github.com/Western-OC2-Lab/Signal-Processing-for-Machine-
Learning. The first part of the section is a demonstration of condition
monitoring of rolling bearings, where the power spectral density (PSD) of
generated vibration is analyzed to extract features indicative of the
operational health of the machine. The second part delves into epilepsy
detection using EEG brain signals, where wavelet packet transform (WPT) is
used to decompose the signals into their elementary modes. Accordingly, the
energy of each mode is calculated, facilitating efficient EEG energy-based
epilepsy detection.

###  VII-A Vibration-Based Condition Monitoring of Rolling Bearings

Vibration-based condition monitoring (VBCM)is commonly used in predictive
maintenance (PdM) due to its inherent advantages over alternative forms of
condition monitoring that include [435, 436]:

  * •

Vibration sensors are non-intrusive and can be contactless, facilitating non-
destructive condition monitoring.

  * •

Real-time acquisition of vibration signals can be conducted in situ, allowing
for online local condition monitoring.

  * •

Vibration sensors are cost-effective and widely available, offering various
specifications to suit various requirements.

  * •

Vibration waveform responds instantly to changes in the monitored condition
and, therefore, is suitable for continuous and intermittent monitoring
applications.

  * •

Of paramount significance, signal processing techniques can be applied to
vibration signals to mitigate corrupting noise and extract weak condition
indications from other masking signals.

The Paderborn University (PU) bearing dataset [437] is used to facilitate a
real-time VBCM. The dataset includes actual vibration signals from a real
system during healthy and faulty operations. The fault types include inner
race (IR), outer race (OR), and combined IR and OR defects. Thus, the dataset
comprises four classes of operational conditions: 1- healthy, 2- IR faults, 3-
OR faults, and 4- combined IR and OR faults.

Figure 30: Sample vibration patterns representing operational conditions in
the PU dataset.

The vibration signals of the dataset were acquired at $64,000$ samples per
second. Hence, in the signal processing pipeline, the vibration signals are
segmented into non-overlapping segments of $N_{o}=12,800$ samples so that the
resultant segment duration is $0.2$ seconds. This duration is selected to
facilitate precise real-time monitoring with moderate computational
requirements. This segmentation results in a dataset of $7,997$ vibration
samples in total. Fig. 30 shows a healthy vibration pattern and faulty
patterns for the PU dataset. The aim is to detect changes in the generated
vibration (oscillation) patterns that may indicate a fault in the equipment.
Here, power spectral analysis helps identify these oscillations since they
appear as dominant frequencies in the PSD. Accordingly, PSDs of the vibration
samples are estimated by Welch’s method using the Hann window and a segment
length of $512$ with $50\%$ overlap. The Number of FFT points (NFFT) is set
equal to $1024$, which is calculated using the conventional method where NFFT
is commonly set to be equal to $2^{P}$, where $P$ is the smallest power of $2$
that is greater than or equal to the Welsh segment length ($512$ samples).
Thus, the value of $p$ is set to $10$. Fig. 31 shows PSD estimates of four
vibration samples that represent healthy and abnormal operational conditions
in the dataset. It is noticeable that a fault alters the PSD characteristics,
and different faults have different effects on the PSD.

Figure 31: PSD estimates of four vibration samples representing healthy and
abnormal operational conditions in the dataset.

It is worth noting that the segment length of $512$ data points used in the
Welsh methods represents a short time duration compared to the duration of the
vibration segment. While such a short duration would reduce frequency
resolution, it increases the number of estimates. This, in turn, helps to
reduce noise [438] and variance of the PSD estimate, leading to a smoother and
more reliable estimate of the PSD, as demonstrated in Fig. 32, which compares
two different estimations of the PSD of a vibration sample.

Figure 32: Two different estimations of the PSD using short and large segments
in the Welsh method.

The first estimation is based on a short segment length of $512$ data points,
while the second estimation employs a larger segment of $6400$ data points.
After PSD estimation, relevant spectral features are extracted from the PSD to
characterize the varying vibration patterns. These features include:

  * •

Spectral Centroid (SC): The SC represents the center of gravity of the
spectral contents of a signal, indicating the average frequency at which the
spectral power is concentrated. Since SC describes the spectral position of
dominant oscillations in the generated vibration, it helps identify healthy
and abnormal vibration patterns. SC is calculated from the PSD using the
following formula [439]:

$CS=\frac{\sum_{k=0}^{K-1}f_{k}P_{k}}{\sum_{k=0}^{K-1}P_{k}}\;\textit{Hz}$
(58)

  * •

Spectral Spread (SS): It describes the deviation of spectral contents with
respect to the SC, providing a measure to assess how dispersed the spectral
power is in relation to the SC. Mathematically, SS is obtained by calculating
the spectral standard deviation with respect to SC [440]:

$SS=\sqrt{\frac{\sum_{k=0}^{K-1}(f_{k}-CS)^{2}P_{k}}{\sum_{k=0}^{K-1}P_{k}}}\;\textit{Hz}$
(59)

The SC and SS are useful spectral features as they describe the position and
the shape of spectral contents [440] and, hence, characterize dominant
oscillatory components within the signal.

  * •

Spectral Entropy (SE): SC is obtained by calculating the Shannon entropy of
the power spectral values, $P_{k}$, to asses the irregularity of vibration
patterns.

$H\left[x[n]\right]=-\sum_{i=0}^{m-1}p\left(x_{i}\right)\,log\left(p\left(x_{i}\right)\right),$
(60)

where, $p\left(x_{i}\right)$ are probabilities associated with $x_{i}$
representing $m$ different values in $x[n]$.Typically, defects generate
vibration with high regularity compared to healthy vibrations [441].

  * •

Peak Power (PP): It represents the maximum value of spectral power in the PSD;
it is expressed mathematically as $max(P_{k}),k=0,1,\dots,K$.

  * •

Peak Frequency (PF): PF is the frequency pin that corresponds to the PP. The
values of PP and PF characterize the dominant spike (maximum peak) in the PSD,
which would be a discriminative indicator of healthy and faulty conditions as
suggested by the comparison of healthy and abnormal PSDs in Fig. 31.

After the feature extraction stage, the resultant set of features is split
into $5,597$ ($70\%$) samples for training and $2,400$ ($30\%$) samples for
testing, and a random forest (RF) classifier is trained accordingly. The
choice of the RF classifier is motivated by its higher performance compared to
other classifiers, as reported in [44]. The achieved performance results and
the confusion matrix (CM) are shown in Table V and Fig. 33, respectively.
Further, a comparison, in terms of achieved accuracy (%), with recent deep
learning (DL)-based methods on the PU dataset is presented in Table VI. The
results show that the engineered features are highly effective in achieving
excellent performance, similar to DL-based methods. Additionally, the signal
processing approach introduced in this section is much more efficient than DL-
based approaches. Specifically, unlike DL approaches, The introduced method
employs a very short duration of the acquired vibration signal (only 0.2
seconds) and results in five features, sufficiently carrying out the tasks of
fault detection and diagnosis. Moreover, in contrast to DL approaches, where
extensive training on a large augmented dataset is required, the introduced
method involves moderate training of an RF classifier.

Table V: Performance results of the proposed and other methods on the PU dataset. Accuracy (%) | F1 score | AUROC
---|---|---
99.42% | 0.995 | 1.00

Figure 33: Confusion matrix (CM) of VBCM of rolling bearings. Table VI: Performance comparison between the proposed signal processing (SP)-based method and other DL-based methods on the PU dataset. Method | Approach | Achieved accuracy (%)
---|---|---
Proposed | SP-based | 99.42%
[442] | DL-based | 99.44%
[443] | DL-based | 97.05%
[444] | DL-based | 96.51%
[445] | DL-based | 99.50%
[446] | DL-based | 96.67%
[447] | DL-based | 97.68%

###  VII-B Epilepsy Detection using EEG Brain Signals

The electroencephalogram (EEG) is a technique for recording electrical
activity arising from the human brain. EEG signals are typically obtained by
placing electrodes on the scalp to measure the differential voltage
fluctuations resulting from ionic current flows within the neurons of the
brain. EEG signals can detect changes over milliseconds [448], thereby
providing insights into the rapid dynamics of brain activity [449]. Thus, they
are commonly used as a medical diagnostic tool for conditions like seizures
and epilepsy due to their high temporal sensitivity. This section introduces a
signal processing-based method for epilepsy detection using EEG signals. The
EEG signals are obtained from the University of Bonn (UoB) EEG dataset [450],
which is a well-known dataset in the field of epilepsy research. The dataset
consists of five subsets, labeled A through E, each containing 100 single-
channel EEG segments of $23.6$ seconds. The signals were recorded with a
sampling rate of $173.61$ Hz, leading to $4097$ data points per signal. sets
C, D, and E were recorded from five patients; EEG signals in set D were taken
from the epileptogenic zone, while set C was recorded from the hippocampal
formation on the opposite hemisphere of the brain. Sets C and D comprise EEG
signals measured during seizure-free intervals (interictal), whereas the EEG
signals in set E were recorded exclusively during seizure activity (ictal)
[451]. Thus, the EEG signal in the dataset can be categorized under three
classes: normal (sets A and B), interictal (sets S and D), and ictal (set E).
Fig. 34 shows an EEG sample from each class.

Figure 34: Sample EEG signals representing the three classes of the UoB
dataset.

The PSD-based method introduced in the previous section is adapted for EEG
certification as a first attempt. The signals are segmented into non-
overlapping segments, with a segment length $N_{o}$ of $500$ data point, which
results in a segmented dataset of $4095$ total EEG samples. With a sampling
rate of $173.61$ Hz, this gives a segment duration of $2.88$ seconds of
duration. For PSD estimation, the Welsh’s segment length is set to
$\frac{N_{o}}{2}$ data points with segment overlap of $\frac{N_{o}}{3}$ data
points; NFFT is set to $1024$. Samples from estimated PSDs are depicted in
Fig. 35.

Figure 35: Samples of estimated PSDs representing the three classes of the UoB
dataset.

Accordingly, SC, SS, SE, PP, and PF features are extracted from the estimated
PSDs. An RF classifier is trained on the extracted features using $70\%$ of
the total samples ($2866$ samples) for training and the remaining $30\%$
samples ($1229$) for testing. The achieved classification results are
$93.409(\%)$, $0.934$, $0.989$ representing, Accuracy (%), F1 score, and
AUROC, respectively.

In contrast to vibrations of rolling bearings, EEG signals are characterized
as low-frequency signals with high temporal sensitivity, making them
particularly susceptible to various forms of artifacts, such as eye and body
movements. This places the need to employ a suitable signal-denoising method
to filter out these artifacts and maintain the frequency range that is of
clinical significance. Typically, EEG components such as infra-slow
oscillations (ISO) (less than $0.5$ Hz) and high-frequency oscillations (HFOs)
(greater than $30$ Hz) are outside the conventional bandwidth of clinical EEG
[452]. Considering this, a band-pass filter with pass and cut-off frequencies
of $0.5$ HZ and $30$ Hz, respectively, is implemented to filter the EEG
signals. Fig. 36 compares the time-domain waveforms, estimated PSDs, and
frequency spectrum of unfiltered (raw) and filtered signals.

Figure 36: A comparison between unfiltered (raw) and filtered EEG signals.

After denoising the signals using the implemented filter, the PSDs of the
filtered signals are estimated, and the features are extracted accordingly.
Table VII shows the achieved results and compares them to those obtained using
the unfiltered signals.

Table VII: Performance results of PSD-based epilepsy detection. Input signal | Accuracy (%) | F1 score | AUROC
---|---|---|---
Raw signal | 93.41% | 0.934 | 0.989
Filtered signal | 94.55% | 0.945 | 0.991

The comparison shows that filtered EEG signals brought a noticeable
improvement in epilepsy detection, demonstrating the effectiveness of the
employed signal-denoising in removing irrelevant frequency components and,
consequently, improving detection accuracy. The CM of the filtered EEG signals
case is presented in Figure 37.

Figure 37: Confusion matrix (CM) of the PSD-based method using filtered EEG
signals.

It can be seen that there are high misclassifications between classes 1 and 2
(normal and interictal) in the CM. Examining PSD contents depicted in Fig. 35
reveals a high degree of similarity between the PSDs of these two classes.
Furthermore, EEG signals are generally nonstationary and nonlinear [453].
These observations suggest that using time-frequency analyses for feature
extraction would capture time-varying dynamics of EEG signals, thereby
improving accuracy compared to pure frequency-domain approaches like PSD-based
analysis. Thus, wavelet decomposition is employed to obtain elementary modes
of EEG signals and the mode’s energies are computed accordingly, This approach
facilitates energy-based analysis with high time-frequency localization to
capture energy-time-frequency varying dynamics within the EEG signal. The
detailed steps of the method include:

  1. 1.

Selection of a proper mother wavelet function to decompose the segmented EEG
signals using WPT to the maximum decomposition level, denoted as $k$. This
step involves obtaining approximation and detail coefficients.

  2. 2.

Use the obtained coefficients to construct elementary modes of the decomposed
signal. This results in $M=2^{k}$ constructed elementary modes with high-time
frequency localization.

  3. 3.

Compute energy $E_{i}$ for each mode:

$E_{i}=\sum_{l=0}^{L-1}|M_{i}[l]|^{2},i=1,2,\dots,M$ (61)

where $L$ is the length of the constructed mode $M_{i}[l]$. Accordingly, a
feature vector of size $S=x\times 2^{K}$ that contains energy values of each
mode is created and fed into the RF classifier.

The selection of the mother wavelet is a critical step in wavelet analysis,
which is often based on empirical evaluation and prior knowledge. In [454], a
comparison is conducted between various mother wavelets to determine the most
suitable wavelet for analyzing EEG signals. Results indicate that $db4$ would
be a proper selection for EEG energy analysis. Such existing results are
particularly beneficial as they set guidelines for the proper selection of
mother wavelets. Hence, using these findings as a guideline, Daubechies
wavelets (db4 - db7) are used to decompose the EEG signals, and energy
features are extracted accordingly.

Figure 38: EEG signal along with some of its constructed elementary modes.

The aim is to empirically evaluate these wavelets to determine the most
suitable one for this application. The obtained results are presented in Table
VIII.

Table VIII: Performance results of wavelet-based epilepsy detection. Mother wavelet | Accuracy (%) | F1 score | AUROC
---|---|---|---
$db4$ | 96.83% | 0.968 | 0.998
$db5$ | 96.95% | 0.969 | 0.997
$db6$ | 96.59% | 0.996 | 0.997
$db7$ | 96.46% | 0.965 | 0.996
Table IX: Performance Results of PSD-based and Wavelet-based Methods for Epilepsy Detection. Approach | Input Signal | Accuracy (%) | F1 score | AUROC
---|---|---|---|---
PSD analysis | Raw signal | 93.41% | 0.934 | 0.989
PSD analysis | Filtered signal | 94.55% | 0.945 | 0.991
WPT-$db4$ | Filtered signal | 96.83% | 0.968 | 0.998
WPT-$db5$ | Filtered signal | 96.95% | 0.969 | 0.997
WPT-$db6$ | Filtered signal | 96.59% | 0.996 | 0.997
WPT-$db7$ | Filtered signal | 96.46% | 0.965 | 0.996
WPT-$db4$ | Raw signal | 97.56% | 0.976 | 0.999
WPT-$db5$ | Raw signal | 98.17% | 0.982 | 0.999
WPT-$db6$ | Raw signal | 98.66% | 0.987 | 0.999
WPT-$db7$ | Raw signal | 97.92% | 0.979 | 0.999

A sample EEG signal and some of its constructed elementary modes are depicted
in Fig38. The performance results show that all wavelets achieved comparable
performance with noticeable improvements compared to PSD-based analysis. These
results are based on filtered EEG signals where irrelevant frequency
components (ISO and HFO) are filtered out. However, in recent years, these
bands gained clinical importance with the advancements in DSP [452]. Motivated
by this, the wavelet analysis is conducted on the unfiltered signals, and
energy features are extracted accordingly. Table IX compares the obtained
results with previous findings, including the results of PSD-based analysis.
The comparison shows that in contrast to PSD-based analysis, where ISO and HFO
components represent irrelevant frequency components, the presence of these
components in wavelet analysis has considerably improved epilepsy detection.
The results demonstrate that wavelet multi-resolution analysis reveals
significant time-frequency dynamics within these bands, underscoring the
significance of including these bands in wavelet analysis.

##  VIII Conclusion

Addressing the existing gaps related to the role of signal processing in ML,
this paper has undertaken a comprehensive, integrated-article approach to
present several contributions that aim to enrich the existing literature.
First, the paper made a solid foundation on the topic through a comprehensive
tutorial on signal processing fundamentals. Written for a diverse readership,
the tutorial allows interested readers to grasp essential concepts and develop
a proper background in signal processing.

Furthermore, the paper provided a comprehensive overview of a typical signal-
processing pipeline, introducing a structured workflow for signal-based ML
applications by categorizing tasks into preprocessing, processing, and
application phases. Additionally, the paper introduced an exhaustive review of
feature extraction methods through a new taxonomy that clearly distinguishes
between two main concepts in feature extraction: feature learning and feature
engineering, thereby offering new insights into the topic of feature
extraction. Focused on signal processing-based feature extraction, the paper
reviewed various available techniques in terms of their main aspects,
advantages, and limitations. The paper also addressed major challenges
associated with the practical deployment of signal-based ML systems, explored
their implications, and highlighted existing and potential solutions.

In an effort to connect the introduced theoretical concepts with real-world
applications, the paper demonstrated the practical application of signal
processing-based ML systems through two use cases: vibration-based condition
monitoring of rolling bearings and epilepsy detection from EEG signals.
Moreover, this work contributes to the research community by introducing a
public repository of relevant Python and MATLAB codes for various signal-
processing techniques.

## References

  * [1] D. K. Iakovidis, M. Ooi, Y. C. Kuang, S. Demidenko, A. Shestakov, V. Sinitsin, M. Henry, A. Sciacchitano, S. Discetti, S. Donati, M. Norgia, A. Menychtas, I. Maglogiannis, S. C. Wriessnegger, L. A. B. Chacon, G. Dimas, D. Filos, A. H. Aletras, J. Töger, F. Dong, S. Ren, A. Uhl, J. Paziewski, J. Geng, F. Fioranelli, R. M. Narayanan, C. Fernandez, C. Stiller, K. Malamousi, S. Kamnis, K. Delibasis, D. Wang, J. Zhang, and R. X. Gao, “Roadmap on signal processing for next generation measurement systems,” _Measurement Science and Technology_ , vol. 33, p. 012002, 1 2022.
  * [2] O. Avci, O. Abdeljaber, S. Kiranyaz, M. Hussein, M. Gabbouj, and D. J. Inman, “A review of vibration-based damage detection in civil structures: From traditional methods to machine learning and deep learning applications,” _Mechanical Systems and Signal Processing_ , vol. 147, p. 107077, 1 2021.
  * [3] J. Leukel, J. González, and M. Riekert, “Adoption of machine learning technology for failure prediction in industrial maintenance: A systematic review,” _Journal of Manufacturing Systems_ , vol. 61, pp. 87–96, 10 2021.
  * [4] C. Zhang, A. A. Mousavi, S. F. Masri, G. Gholipour, K. Yan, and X. Li, “Vibration feature extraction using signal processing techniques for structural health monitoring: A review,” _Mechanical Systems and Signal Processing_ , vol. 177, p. 109175, 9 2022.
  * [5] M. Romanssini, P. C. C. de Aguirre, L. Compassi-Severo, and A. G. Girardi, “A review on vibration monitoring techniques for predictive maintenance of rotating machinery,” _Eng_ , vol. 4, pp. 1797–1817, 6 2023.
  * [6] O. Matania, L. Bachar, E. Bechhoefer, and J. Bortman, “Signal processing for the condition-based maintenance of rotating machines via vibration analysis: A tutorial,” _Sensors_ , vol. 24, p. 454, 1 2024.
  * [7] S. Sonawani, K. Patil, and P. Natarajan, “Biomedical signal processing for health monitoring applications: a review,” _International Journal of Applied Systemic Studies_ , vol. 10, p. 44, 2023.
  * [8] Z. Khademi, F. Ebrahimi, and H. M. Kordy, “A review of critical challenges in mi-bci: From conventional to deep learning methods,” _Journal of Neuroscience Methods_ , vol. 383, p. 109736, 1 2023.
  * [9] V. Gupta, M. Mittal, V. Mittal, and N. K. Saxena, “A critical review of feature extraction techniques for ecg signal analysis,” _Journal of The Institution of Engineers (India): Series B_ , vol. 102, pp. 1049–1060, 10 2021.
  * [10] L. Boubchir, B. Daachi, and V. Pangracious, “A review of feature extraction for eeg epileptic seizure detection and classification.” IEEE, 7 2017, pp. 456–460.
  * [11] R. Yuvaraj, P. Thagavel, J. Thomas, J. Fogarty, and F. Ali, “Comprehensive analysis of feature extraction methods for emotion recognition from multichannel eeg recordings,” _Sensors_ , vol. 23, p. 915, 1 2023.
  * [12] R. Jenke, A. Peer, and M. Buss, “Feature extraction and selection for emotion recognition from eeg,” _IEEE Transactions on Affective Computing_ , vol. 5, pp. 327–339, 7 2014.
  * [13] A. Chaddad, Y. Wu, R. Kateb, and A. Bouridane, “Electroencephalography signal processing: A comprehensive review and analysis of methods and techniques,” _Sensors_ , vol. 23, p. 6434, 7 2023.
  * [14] M. L. Duc, P. Bilik, and R. Martinek, “Harmonics signal feature extraction techniques: A review,” _Mathematics_ , vol. 11, p. 1877, 4 2023.
  * [15] J. de Lope and M. Graña, “An ongoing review of speech emotion recognition,” _Neurocomputing_ , vol. 528, pp. 1–11, 4 2023.
  * [16] S. Pangaonkar and A. Panat, _A Review of Various Techniques Related to Feature Extraction and Classification for Speech Signal Analysis_ , 2020, pp. 534–549.
  * [17] S. Nivetha, “A survey on speech feature extraction and classification techniques.” IEEE, 2 2020, pp. 48–53.
  * [18] G. Sharma, K. Umapathy, and S. Krishnan, “Trends in audio signal feature extraction methods,” _Applied Acoustics_ , vol. 158, p. 107020, 1 2020.
  * [19] A. A. Anthony and C. M. Patil, “Speech emotion recognition systems: A comprehensive review on different methodologies,” _Wireless Personal Communications_ , vol. 130, pp. 515–525, 5 2023.
  * [20] W. Liu, Y. Liu, S. Li, and Y. Chen, “A review of variational mode decomposition in seismic data analysis,” _Surveys in Geophysics_ , vol. 44, pp. 323–355, 4 2023.
  * [21] S. M. Mousavi and G. C. Beroza, “Machine learning in earthquake seismology,” _Annual Review of Earth and Planetary Sciences_ , vol. 51, pp. 105–129, 5 2023.
  * [22] P. Choudhary, N. Goel, and M. Saini, “A survey on seismic sensor based target detection, localization, identification, and activity recognition,” _ACM Computing Surveys_ , vol. 55, pp. 1–36, 11 2023.
  * [23] A. Rojas and G. J. Dolecek, _A Review of Spectrum Sensing Techniques Based on Machine Learning_ , 7 2024, pp. 1–21.
  * [24] Q.-V. Pham, N. T. Nguyen, T. Huynh-The, L. B. Le, K. Lee, and W.-J. Hwang, “Intelligent radio signal processing: A survey,” _IEEE Access_ , vol. 9, pp. 83 818–83 850, 2021.
  * [25] N. Soltanieh, Y. Norouzi, Y. Yang, and N. C. Karmakar, “A review of radio frequency fingerprinting techniques,” _IEEE Journal of Radio Frequency Identification_ , vol. 4, pp. 222–233, 9 2020.
  * [26] Y. Li and L. Wang, “A survey of radio frequency fingerprint feature extraction and recognition based on deep learning.” Institution of Engineering and Technology, 2022, pp. 776–782.
  * [27] T. Wang, G. Yang, P. Chen, Z. Xu, M. Jiang, and Q. Ye, “A survey of applications of deep learning in radio signal modulation recognition,” _Applied Sciences_ , vol. 12, p. 12052, 11 2022.
  * [28] A. Hazza, M. Shoaib, S. A. Alshebeili, and A. Fahad, “An overview of feature-based methods for digital modulation classification.” IEEE, 2 2013, pp. 1–6.
  * [29] S. Peng, S. Sun, and Y.-D. Yao, “A survey of modulation classification using deep learning: Signal representation and data preprocessing,” _IEEE Transactions on Neural Networks and Learning Systems_ , vol. 33, pp. 7020–7038, 12 2022.
  * [30] S. Xie and J. Ye, “Overview of automatic modulation recognition methods.” IEEE, 4 2023, pp. 1–7.
  * [31] R. Priemer, _Introductory Signal Processing_. WORLD SCIENTIFIC, 11 1990.
  * [32] R. X. Gao and R. Yan, _Signals and Signal Processing in Manufacturing_. Springer US, 2011, pp. 1–15.
  * [33] L. F. Chaparro and A. Akan, _Frequency Analysis: The Fourier Series_. Elsevier, 2019, pp. 241–303.
  * [34] S. Braun, _SPECTRAL ANALYSIS, CLASSICAL METHODS_. Elsevier, 2001, pp. 1208–1223.
  * [35] D. L. Massart, B. G. M. Vandeginste, S. N. Deming, Y. Michotte, and L. Kaufman, Eds., _Chapter 12 - Signals and Data_. Elsevier, 2003, vol. 2, pp. 157–163. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0922348708702259
  * [36] A. Stepchenko, J. Chizhov, L. Aleksejeva, and J. Tolujew, “Nonlinear, non-stationary and seasonal time series forecasting using different methods coupled with data preprocessing,” _Procedia Computer Science_ , vol. 104, pp. 578–585, 2017.
  * [37] H. Landau, “Sampling, data transmission, and the nyquist rate,” _Proceedings of the IEEE_ , vol. 55, pp. 1701–1706, 1967.
  * [38] G. Ellis, _The z-Domain_. Elsevier, 2012, pp. 73–96.
  * [39] A. Neupane, N. Raj, R. Deo, and M. Ali, _Development of data-driven models for wind speed forecasting in Australia_. Elsevier, 2021, pp. 143–190.
  * [40] C. E. Shannon, “A mathematical theory of communication,” _Bell System Technical Journal_ , vol. 27, pp. 379–423, 7 1948.
  * [41] Y. Li, X. Wang, S. Si, and S. Huang, “Entropy based fault classification using the case western reserve university data: A benchmark study,” _IEEE Transactions on Reliability_ , vol. 69, pp. 754–767, 6 2020.
  * [42] B. Ricaud and B. Torrésani, “A survey of uncertainty principles and some signal processing applications,” _Advances in Computational Mathematics_ , vol. 40, pp. 629–650, 6 2014.
  * [43] P. Welch, “The use of fast fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms,” _IEEE Transactions on Audio and Electroacoustics_ , vol. 15, pp. 70–73, 6 1967.
  * [44] S. A. Aburakhia, R. Myers, and A. Shami, “A hybrid method for condition monitoring and fault diagnosis of rolling bearings with low system delay,” _IEEE Transactions on Instrumentation and Measurement_ , vol. 71, pp. 1–13, 2022.
  * [45] D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” _Biometrika_ , vol. 81, pp. 425–455, 9 1994.
  * [46] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis,” _Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences_ , vol. 454, pp. 903–995, 3 1998.
  * [47] W. Guo and M. J. Zuo, _Adaptive Signal Decomposition Methods for Vibration Signals of Rotating Machinery_. InTech, 5 2017.
  * [48] M. Zare and N. M. Nouri, “End-effects mitigation in empirical mode decomposition using a new correlation-based expansion model,” _Mechanical Systems and Signal Processing_ , vol. 194, p. 110205, 7 2023.
  * [49] Y. Gao, G. Ge, Z. Sheng, and E. Sang, “Analysis and solution to the mode mixing phenomenon in emd.” IEEE, 2008, pp. 223–227.
  * [50] Z. WU and N. E. HUANG, “Ensemble empirical mode decomposition: A noise-assisted data analysis method,” _Advances in Adaptive Data Analysis_ , vol. 01, pp. 1–41, 1 2009.
  * [51] K. Dragomiretskiy and D. Zosso, “Variational mode decomposition,” _IEEE Transactions on Signal Processing_ , vol. 62, pp. 531–544, 2 2014.
  * [52] J. S. Smith, “The local mean decomposition and its application to eeg perception data,” _Journal of The Royal Society Interface_ , vol. 2, pp. 443–454, 12 2005.
  * [53] J. Gilles, “Empirical wavelet transform,” _IEEE Transactions on Signal Processing_ , vol. 61, pp. 3999–4010, 8 2013.
  * [54] T. Eriksen and N. ur Rehman, “Data-driven nonstationary signal decomposition approaches: a comparative analysis,” _Scientific Reports_ , vol. 13, p. 1798, 1 2023.
  * [55] M. Civera and C. Surace, “A comparative analysis of signal decomposition techniques for structural health monitoring on an experimental benchmark,” _Sensors_ , vol. 21, p. 1825, 3 2021.
  * [56] Z. Feng, D. Zhang, and M. J. Zuo, “Adaptive mode decomposition methods and their applications in signal analysis for machinery fault diagnosis: A review with examples,” _IEEE Access_ , vol. 5, pp. 24 301–24 331, 2017.
  * [57] T. Liu, Z. Luo, J. Huang, and S. Yan, “A comparative study of four kinds of adaptive decomposition algorithms and their applications,” _Sensors_ , vol. 18, p. 2120, 7 2018.
  * [58] G. Lindfield and J. Penny, _Analyzing Data Using Discrete Transforms_. Elsevier, 2019, pp. 383–431.
  * [59] A. Tabrizi, L. Garibaldi, A. Fasana, and S. Marchesiello, _Influence of Stopping Criterion for Sifting Process of Empirical Mode Decomposition (EMD) on Roller Bearing Fault Diagnosis_ , 2014, pp. 389–398.
  * [60] M. Ali, D. M. Khan, I. Saeed, and H. M. Alshanbari, “A new approach to empirical mode decomposition based on akima spline interpolation technique,” _IEEE Access_ , vol. 11, pp. 67 370–67 384, 2023.
  * [61] L. Cohen, _Time-frequency analysis_. Prentice hall New Jersey, 1995, vol. 778.
  * [62] J. E. Torres-Fernández, A. Prieto-Guerrero, and G. Espinosa-Paredes, “Decay ratio estimation using the instantaneous autocorrelation function,” _Nuclear Engineering and Design_ , vol. 240, pp. 3559–3570, 10 2010.
  * [63] F. Hlawatsch and G. Boudreaux-Bartels, “Linear and quadratic time-frequency signal representations,” _IEEE Signal Processing Magazine_ , vol. 9, pp. 21–67, 4 1992.
  * [64] Y. Wu and X. Li, “Elimination of cross‐terms in the wigner–ville distribution of multi‐component lfm signals,” _IET Signal Processing_ , vol. 11, pp. 657–662, 8 2017.
  * [65] P. Flandrin, “Some features of time-frequency representations of multicomponent signals,” in _ICASSP ’84. IEEE International Conference on Acoustics, Speech, and Signal Processing_ , vol. 9, 1984, pp. 266–269.
  * [66] ——, _Time-frequency time-scale analysis_. Academic press, 1998.
  * [67] H.-I. Choi and W. Williams, “Improved time-frequency representation of multicomponent signals using exponential kernels,” _IEEE Transactions on Acoustics, Speech, and Signal Processing_ , vol. 37, pp. 862–871, 6 1989.
  * [68] Y. Zhao, L. Atlas, and R. Marks, “The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals,” _IEEE Transactions on Acoustics, Speech, and Signal Processing_ , vol. 38, pp. 1084–1091, 7 1990.
  * [69] N. Abdennour, T. Ouni, and N. B. Amor, “The importance of signal pre-processing for machine learning: The influence of data scaling in a driver identity classification.” IEEE, 11 2021, pp. 1–6.
  * [70] N. Mourad, “Robust smoothing of one‐dimensional data with missing and/or outlier values,” _IET Signal Processing_ , vol. 15, pp. 323–336, 7 2021.
  * [71] A. Savitzky and M. J. E. Golay, “Smoothing and differentiation of data by simplified least squares procedures.” _Analytical Chemistry_ , vol. 36, pp. 1627–1639, 7 1964.
  * [72] S. R. Krishnan and C. S. Seelamantula, “On the selection of optimum savitzky-golay filters,” _IEEE Transactions on Signal Processing_ , vol. 61, pp. 380–391, 1 2013.
  * [73] Tanu and D. Kakkar, “Accounting for order-frame length tradeoff of savitzky-golay smoothing filters.” IEEE, 2 2018, pp. 805–810.
  * [74] K. C. B. Rao and B. T. Krishna, “Comparative analysis of integer and non-integer order savitzky-golay digital filters.” IEEE, 1 2017, pp. 26–31.
  * [75] X. Lv, F. Zhou, B. Li, and B. Yan, “Incipient fault feature extraction of rolling bearing based on signal reconstruction,” _Electronics_ , vol. 12, p. 3749, 9 2023.
  * [76] I. M. A. Wirawan, R. Wardoyo, D. Lelono, and S. Kusrohmaniah, “Comparison of smoothing methods to remove artifacts in emotion recognition based on electroencephalogram signals.” IEEE, 12 2022, pp. 1–8.
  * [77] P. D. Rosero-Montalvo, V. F. López-Batista, and D. H. Peluffo-Ordóñez, “A new data-preprocessing-related taxonomy of sensors for iot applications,” _Information_ , vol. 13, p. 241, 5 2022.
  * [78] A. Kawala-Sterniuk, M. Podpora, M. Pelc, M. Blaszczyszyn, E. J. Gorzelanczyk, R. Martinek, and S. Ozana, “Comparison of smoothing filters in analysis of eeg data for the medical diagnostics purposes,” _Sensors_ , vol. 20, p. 807, 2 2020.
  * [79] P. Kowalski and R. Smyk, “Review and comparison of smoothing algorithms for one-dimensional data noise reduction.” IEEE, 5 2018, pp. 277–281.
  * [80] H. W. Ott, _Noise reduction techniques in electronic systems_ , 2nd ed. Wiley-Interscience, 1988, vol. 442.
  * [81] V. J. Barclay, R. F. Bonner, and I. P. Hamilton, “Application of wavelet transforms to experimental spectra: Smoothing, denoising, and data set compression,” _Analytical Chemistry_ , vol. 69, pp. 78–90, 1 1997.
  * [82] H. Ashraf, A. Waris, M. Jamil, S. O. Gilani, I. K. Niazi, E. N. Kamavuako, and S. H. N. Gilani, “Determination of optimum segmentation schemes for pattern recognition-based myoelectric control: A multi-dataset investigation,” _IEEE Access_ , vol. 8, pp. 90 862–90 877, 2020.
  * [83] A. Dehghani, O. Sarbishei, T. Glatard, and E. Shihab, “A quantitative comparison of overlapping and non-overlapping sliding windows for human activity recognition using inertial sensors,” _Sensors_ , vol. 19, p. 5026, 11 2019.
  * [84] B. Fida, I. Bernabucci, D. Bibbo, S. Conforto, and M. Schmid, “Varying behavior of different window sizes on the classification of static and dynamic physical activities from a single accelerometer,” _Medical Engineering and Physics_ , vol. 37, pp. 705–711, 7 2015.
  * [85] V. J. D. Vieira, S. C. Costa, and S. E. N. Correia, “Non-stationarity-based adaptive segmentation applied to voice disorder discrimination,” _IEEE Access_ , vol. 11, pp. 54 750–54 759, 2023.
  * [86] M. M. Milani, P. E. Abas, and L. C. D. Silva, “A critical review of heart sound signal segmentation algorithms,” _Smart Health_ , vol. 24, p. 100283, 6 2022.
  * [87] K. Chang, Y. Yoo, and J.-G. Baek, “Anomaly detection using signal segmentation and one-class classification in diffusion process of semiconductor manufacturing,” _Sensors_ , vol. 21, p. 3880, 6 2021.
  * [88] J. Jirka, M. Prauzek, O. Krejcar, and K. Kuca, “Automatic epilepsy detection using fractal dimensions segmentation and gp-svm classification,” _Neuropsychiatric Disease and Treatment_ , vol. Volume 14, pp. 2439–2449, 9 2018.
  * [89] M. H. M. Noor, Z. Salcic, and K. I.-K. Wang, “Adaptive sliding window segmentation for physical activity recognition using a single tri-axial accelerometer,” _Pervasive and Mobile Computing_ , vol. 38, pp. 41–59, 7 2017.
  * [90] S. Bombiński, K. Błażejak, M. Nejman, and K. Jemielniak, “Sensor signal segmentation for tool condition monitoring,” _Procedia CIRP_ , vol. 46, pp. 155–160, 2016.
  * [91] A. Prochazka, M. Mudrova, O. Vysata, R. Hava, and C. P. S. Araujo, “Multi-channel eeg signal segmentation and feature extraction.” IEEE, 5 2010, pp. 317–320.
  * [92] H. O. A. Ahmed and A. K. Nandi, “Vibration image representations for fault diagnosis of rotating machines: A review,” _Machines_ , vol. 10, p. 1113, 11 2022.
  * [93] C.-L. Yang, Z.-X. Chen, and C.-Y. Yang, “Sensor classification using convolutional neural network by encoding multivariate time series as two-dimensional colored images,” _Sensors_ , vol. 20, p. 168, 12 2019.
  * [94] N. Sobahi, B. Ari, H. Cakar, O. F. Alcin, and A. Sengur, “A new signal to image mapping procedure and convolutional neural networks for efficient schizophrenia detection in eeg recordings,” _IEEE Sensors Journal_ , vol. 22, pp. 7913–7919, 4 2022.
  * [95] L. Guo, Z. Lu, X. Wen, S. Zhou, and Z. Han, “From signal to image: Capturing fine-grained human poses with commodity wi-fi,” _IEEE Communications Letters_ , vol. 24, pp. 802–806, 4 2020.
  * [96] P. Singh, P. Pandey, K. Miyapuram, and S. Raman, “Eeg2image: Image reconstruction from eeg brain signals.” IEEE, 6 2023, pp. 1–5.
  * [97] K. Gupta and Z. Wei, “Rm-net: Rasterizing markov signals to images for deep learning.” IEEE, 10 2023, pp. 654–659.
  * [98] C. M. Yilmaz, B. H. Yilmaz, and C. Kose, “A novel signal-to-image conversion approach with ensembles of pretrained cnns for motor imagery eeg signals.” IEEE, 9 2023, pp. 49–53.
  * [99] J. Venton, P. J. Aston, N. A. S. Smith, and P. M. Harris, “Signal to image to classification: Transfer learning for ecg.” IEEE, 7 2020, pp. 1–2.
  * [100] B. H. Yilmaz, C. M. Yilmaz, and C. Kose, “Classification of the eeg signals for the cursor movement with the signal-to-image transformation.” IEEE, 10 2019, pp. 1–4.
  * [101] T. Tayeh, S. Aburakhia, R. Myers, and A. Shami, “An attention-based convlstm autoencoder with dynamic thresholding for unsupervised anomaly detection in multivariate time series,” _Machine Learning and Knowledge Extraction_ , vol. 4, no. 2, pp. 350–370, 2022. [Online]. Available: https://www.mdpi.com/2504-4990/4/2/15
  * [102] L. Yang and A. Shami, “A transfer learning and optimized cnn based intrusion detection system for internet of vehicles,” in _ICC 2022 - IEEE International Conference on Communications_ , 2022, pp. 2774–2779.
  * [103] A. Moubayed, M. Sharif, M. Luccini, S. Primak, and A. Shami, “Water leak detection survey: Challenges and research opportunities using data fusion and federated learning,” _IEEE Access_ , vol. 9, pp. 40 595–40 611, 2021.
  * [104] M. Injadat, A. Moubayed, A. B. Nassif, and A. Shami, “Machine learning towards intelligent systems: applications, challenges, and opportunities,” _Artificial Intelligence Review_ , vol. 54, pp. 3299–3348, 6 2021.
  * [105] L. Yang and A. Shami, “Iot data analytics in dynamic environments: From an automated machine learning perspective,” _Engineering Applications of Artificial Intelligence_ , vol. 116, p. 105366, 2022. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0952197622003803
  * [106] ——, “On hyperparameter optimization of machine learning algorithms: Theory and practice,” _Neurocomputing_ , vol. 415, pp. 295–316, 2020. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0925231220311693
  * [107] ——, “A multi-stage automated online network data stream analytics framework for iiot systems,” _IEEE Transactions on Industrial Informatics_ , vol. 19, no. 2, pp. 2107–2116, 2023.
  * [108] V. Narayan, S. Awasthi, N. Fatima, M. Faiz, and S. Srivastava, “Deep learning approaches for human gait recognition: A review.” IEEE, 2 2023, pp. 763–768.
  * [109] S. Ahmad, K. Styp-Rekowski, S. Nedelkoski, and O. Kao, “Autoencoder-based condition monitoring and anomaly detection method for rotating machines.” IEEE, 2 2020, pp. 4093–4102.
  * [110] M. Liao, C. Liu, C. Wang, and J. Yang, “Research on a rolling bearing fault detection method with wavelet convolution deep transfer learning,” _IEEE Access_ , vol. 9, pp. 45 175–45 188, 2021.
  * [111] D. Hassan, H. I. Hussein, and M. M. Hassan, “Heart disease prediction based on pre-trained deep neural networks combined with principal component analysis,” _Biomedical Signal Processing and Control_ , vol. 79, p. 104019, 2 2023.
  * [112] Q. Nawaz, M. Younas, I. Hamid, and S. M. M. Gilani, “Recurrent neural network based human emotion recognition using eeg brain signals.” IEEE, 2 2023, pp. 117–122.
  * [113] F. S. Butt, M. F. Wagner, J. Schafer, and D. G. Ullate, “Toward automated feature extraction for deep learning classification of electrocardiogram signals,” _IEEE Access_ , vol. 10, pp. 118 601–118 616, 2022.
  * [114] S. S. Xu, M.-W. Mak, and C.-C. Cheung, “Towards end-to-end ecg classification with raw signal extraction and deep neural networks,” _IEEE Journal of Biomedical and Health Informatics_ , vol. 23, pp. 1574–1584, 2 2019.
  * [115] W. Chen, H. Zhou, L. Cheng, and M. Xia, “Condition monitoring and anomaly detection of wind turbines using temporal convolutional informer and robust dynamic mahalanobis distance,” _IEEE Transactions on Instrumentation and Measurement_ , vol. 72, pp. 1–14, 2023.
  * [116] A. Mohammad-Alikhani, B. Nahid-Mobarakeh, and M.-F. Hsieh, “One-dimensional lstm-regulated deep residual network for data-driven fault detection in electric machines,” _IEEE Transactions on Industrial Electronics_ , vol. 71, pp. 3083–3092, 2 2024.
  * [117] D. Zhang, Y. Lu, Y. Li, W. Ding, B. Zhang, and J. Xiao, “Frequency learning attention networks based on deep learning for automatic modulation classification in wireless communication,” _Pattern Recognition_ , vol. 137, p. 109345, 2 2023.
  * [118] B. Zali-Vargahan, A. Charmin, H. Kalbkhani, and S. Barghandan, “Deep time-frequency features and semi-supervised dimension reduction for subject-independent emotion recognition from multi-channel eeg signals,” _Biomedical Signal Processing and Control_ , vol. 85, p. 104806, 2 2023.
  * [119] W. Jia, M. Sun, J. Lian, and S. Hou, “Feature dimensionality reduction: a review,” _Complex and Intelligent Systems_ , vol. 8, pp. 2663–2693, 2 2022.
  * [120] M. Jalayer, C. Orsenigo, and C. Vercellis, “Fault detection and diagnosis for rotating machinery: A model based on convolutional lstm, fast fourier and continuous wavelet transforms,” _Computers in Industry_ , vol. 125, p. 103378, 2 2021.
  * [121] Y. Zhang, K. Xing, R. Bai, D. Sun, and Z. Meng, “An enhanced convolutional neural network for bearing fault diagnosis based on time–frequency image,” _Measurement_ , vol. 157, p. 107667, 2 2020.
  * [122] H. V. Dang, H. Tran-Ngoc, T. V. Nguyen, T. Bui-Tien, G. D. Roeck, and H. X. Nguyen, “Data-driven structural health monitoring using feature fusion and hybrid deep learning,” _IEEE Transactions on Automation Science and Engineering_ , vol. 18, pp. 2087–2103, 2 2021.
  * [123] K. Zaman, M. Sah, C. Direkoglu, and M. Unoki, “A survey of audio classification using deep learning,” _IEEE Access_ , vol. 11, pp. 106 620–106 649, 2023.
  * [124] Y. Miao, Y. V. Zakharov, H. Sun, J. Li, and J. Wang, “Underwater acoustic signal classification based on sparse time–frequency representation and deep learning,” _IEEE Journal of Oceanic Engineering_ , vol. 46, pp. 952–962, 2 2021.
  * [125] N. P. G. Seshadri, S. Agrawal, B. K. Singh, B. Geethanjali, V. Mahesh, and R. B. Pachori, “Eeg based classification of children with learning disabilities using shallow and deep neural network,” _Biomedical Signal Processing and Control_ , vol. 82, p. 104553, 2 2023.
  * [126] H. Altaheri, G. Muhammad, M. Alsulaiman, S. U. Amin, G. A. Altuwaijri, W. Abdul, M. A. Bencherif, and M. Faisal, “Deep learning techniques for classification of electroencephalogram (eeg) motor imagery (mi) signals: a review,” _Neural Computing and Applications_ , vol. 35, pp. 14 681–14 722, 2 2023.
  * [127] L. Ilias, D. Askounis, and J. Psarras, “Multimodal detection of epilepsy with deep neural networks,” _Expert Systems with Applications_ , vol. 213, p. 119010, 2 2023.
  * [128] S.-H. Kim, C.-B. Moon, J.-W. Kim, and D.-S. Kim, “A hybrid deep learning model for automatic modulation classification,” _IEEE Wireless Communications Letters_ , vol. 11, pp. 313–317, 2 2022.
  * [129] S. Zheng, X. Zhou, L. Zhang, P. Qi, K. Qiu, J. Zhu, and X. Yang, “Toward next-generation signal intelligence: A hybrid knowledge and data-driven deep learning framework for radio signal classification,” _IEEE Transactions on Cognitive Communications and Networking_ , vol. 9, pp. 564–579, 2 2023.
  * [130] S. Peng, S. Sun, and Y.-D. Yao, “A survey of modulation classification using deep learning: Signal representation and data preprocessing,” _IEEE Transactions on Neural Networks and Learning Systems_ , vol. 33, pp. 7020–7038, 2 2022.
  * [131] T. Chen, S. Gao, S. Zheng, S. Yu, Q. Xuan, C. Lou, and X. Yang, “Emd and vmd empowered deep learning for radio modulation recognition,” _IEEE Transactions on Cognitive Communications and Networking_ , vol. 9, pp. 43–57, 2 2023.
  * [132] W. Li, K. Wang, L. You, and Z. Huang, “A new deep learning framework for hf signal detection in wideband spectrogram,” _IEEE Signal Processing Letters_ , vol. 29, pp. 1342–1346, 2022.
  * [133] K. Qiu, S. Zheng, L. Zhang, C. Lou, and X. Yang, “Deepsig: A hybrid heterogeneous deep learning framework for radio signal classification,” _IEEE Transactions on Wireless Communications_ , p. 1, 2023.
  * [134] Y. Lei, Z. He, and Y. Zi, “A new approach to intelligent fault diagnosis of rotating machinery,” _Expert Systems with Applications_ , vol. 35, pp. 1593–1600, 2 2008.
  * [135] B. R. Nayana and P. Geethanjali, “Analysis of statistical time-domain features effectiveness in identification of bearing faults from vibration signal,” _IEEE Sensors Journal_ , vol. 17, pp. 5618–5625, 2 2017.
  * [136] P. Geethanjali, Y. K. Mohan, and J. Sen, “Time domain feature extraction and classification of eeg data for brain computer interface.” IEEE, 2 2012, pp. 1136–1139.
  * [137] X. Wang, Y. Zheng, Z. Zhao, and J. Wang, “Bearing fault diagnosis based on statistical locally linear embedding,” _Sensors_ , vol. 15, pp. 16 225–16 247, 2 2015.
  * [138] S. M. S. Moctar, I. Rida, and S. Boudaoud, “Time-domain features for semg signal classification: A brief survey,” _JETSAN 2023_ , 2023.
  * [139] A. Mert, N. Kılıç, and A. Akan, “Evaluation of bagging ensemble method with time-domain feature extraction for diagnosing of arrhythmia beats,” _Neural Computing and Applications_ , vol. 24, pp. 317–326, 2 2014.
  * [140] S. U. Jan, Y.-D. Lee, J. Shin, and I. Koo, “Sensor fault classification based on support vector machine and statistical time-domain features,” _IEEE Access_ , vol. 5, pp. 8682–8690, 2017.
  * [141] D. Tkach, H. Huang, and T. A. Kuiken, “Study of stability of time-domain features for electromyographic pattern recognition,” _Journal of NeuroEngineering and Rehabilitation_ , vol. 7, p. 21, 2 2010.
  * [142] B. Sreejith, A. K. Verma, and A. Srividya, “Fault diagnosis of rolling element bearing using time-domain features and neural networks.” IEEE, 2 2008, pp. 1–6.
  * [143] Y. Paul, V. Goyal, and R. A. Jaswal, “Comparative analysis between svm and knn classifier for emg signal classification on elementary time domain features.” IEEE, 2 2017, pp. 169–175.
  * [144] R. Barioul, S. Fakhfakh, H. Derbel, and O. Kanoun, “Evaluation of emg signal time domain features for hand gesture distinction.” IEEE, 2 2019, pp. 489–493.
  * [145] F. O.K. and R. R., “Time-domain exponential energy for epileptic eeg signal classification,” _Neuroscience Letters_ , vol. 694, pp. 1–8, 2 2019.
  * [146] K. Nazarpour, A. R. Sharafat, and S. M. Firoozabadi, “A novel feature extraction scheme for myoelectric signals classification using higher order statistics.” IEEE, pp. 293–296.
  * [147] K. Nazarpour, A. R. Sharafat, and S. M. P. Firoozabadi, “Application of higher order statistics to surface electromyogram signal classification,” _IEEE Transactions on Biomedical Engineering_ , vol. 54, pp. 1762–1769, 2 2007.
  * [148] J. Chen, B. Xu, and X. Zhang, “A vibration feature extraction method based on time-domain dimensional parameters and mahalanobis distance,” _Mathematical Problems in Engineering_ , vol. 2021, pp. 1–12, 7 2021.
  * [149] A. Saci, A. Al-Dweik, and A. Shami, “Autocorrelation integrated gaussian based anomaly detection using sensory data in industrial manufacturing,” _IEEE Sensors Journal_ , vol. 21, no. 7, pp. 9231–9241, 2021.
  * [150] E. Ali, R. K. Udhayakumar, M. Angelova, and C. Karmakar, “Performance analysis of entropy methods in detecting epileptic seizure from surface electroencephalograms.” IEEE, 2 2021, pp. 1082–1085.
  * [151] W. Jiao, G. Li, Y. Jiang, R. Baim, C. Tang, T. Yan, X. Ding, and Y. Yan, “Multi-scale sample entropy-based energy moment features applied to fault classification,” _IEEE Access_ , vol. 9, pp. 8444–8454, 2021.
  * [152] C. Liang and C. Chen, “Generalized composite multiscale diversity entropy and its application for fault diagnosis of rolling bearing in automotive production line,” _IEEE Access_ , vol. 9, pp. 84 545–84 558, 2021.
  * [153] M. Li and W. Chen, “Fft-based deep feature learning method for eeg classification,” _Biomedical Signal Processing and Control_ , vol. 66, p. 102492, 2 2021.
  * [154] N. F. Güler and S. Koçer, “Classification of emg signals using pca and fft,” _Journal of Medical Systems_ , vol. 29, pp. 241–250, 2 2005.
  * [155] M. K. Delimayanti, B. Purnama, N. G. Nguyen, M. R. Faisal, K. R. Mahmudah, F. Indriani, M. Kubo, and K. Satou, “Classification of brainwaves for sleep stages by high-dimensional fft features from eeg signals,” _Applied Sciences_ , vol. 10, p. 1797, 2 2020.
  * [156] E. C. Djamal, W. I. Furi, and F. Nugraha, “Detection of eeg signal post-stroke using fft and convolutional neural network.” IEEE, 2 2019, pp. 18–23.
  * [157] H. Arabaci and A. Mohamed, “A knowledge-based diagnosis algorithm for broken rotor bar fault classification using fft, principal component analysis and support vector machines,” _International Journal of Intelligent Engineering Informatics_ , vol. 8, p. 19, 2020.
  * [158] C. Altın and O. Er, “Comparison of different time and frequency domain feature extraction methods on elbow gesture’s emg,” _European Journal of Interdisciplinary Studies_ , vol. 2, p. 35, 2 2016.
  * [159] S. K. Narudin, N. M. Nasir, A. Joret, N. Fuad, B. S. K. K. Ibrahim, and M. S. Huq, “Classification of hand movements of stroke patients using combination of statistical features and artificial neural network,” 2023, p. 60011.
  * [160] L. S. Dhamande and M. B. Chaudhari, “Compound gear-bearing fault feature extraction using statistical features based on time-frequency method,” _Measurement_ , vol. 125, pp. 63–77, 2 2018.
  * [161] M. Murugappan and S. Murugappan, “Human emotion recognition through short time electroencephalogram (eeg) signals using fast fourier transform (fft).” IEEE, 2 2013, pp. 289–294.
  * [162] S. A. Shufni and M. Y. Mashor, “Ecg signals classification based on discrete wavelet transform, time domain and frequency domain features.” IEEE, 2 2015, pp. 1–6.
  * [163] M. Altaf, T. Akram, M. A. Khan, M. Iqbal, M. M. I. Ch, and C.-H. Hsu, “A new statistical features based approach for bearing fault diagnosis using vibration signals,” _Sensors_ , vol. 22, p. 2012, 2 2022.
  * [164] L. Jiang, J. He, H. Pan, D. Wu, T. Jiang, and J. Liu, “Seizure detection algorithm based on improved functional brain network structure feature extraction,” _Biomedical Signal Processing and Control_ , vol. 79, p. 104053, 2 2023.
  * [165] P. Singh, S. D. Joshi, R. K. Patney, and K. Saha, “Fourier-based feature extraction for classification of eeg signals using eeg rhythms,” _Circuits, Systems, and Signal Processing_ , vol. 35, pp. 3700–3715, 2 2016.
  * [166] M. N. Alam, M. I. Ibrahimy, and S. M. A. Motakabber, “Feature extraction of eeg signal by power spectral density for motor imagery based bci.” IEEE, 2 2021, pp. 234–237.
  * [167] Q. Gao, A. H. Omran, Y. Baghersad, O. Mohammadi, M. A. Alkhafaji, A. K. J. Al-Azzawi, S. H. Al-Khafaji, N. Emami, D. Toghraie, and M. J. Golkar, “Electroencephalogram signal classification based on fourier transform and pattern recognition network for epilepsy diagnosis,” _Engineering Applications of Artificial Intelligence_ , vol. 123, p. 106479, 2 2023.
  * [168] A. Zhang, B. Yang, and L. Huang, “Feature extraction of eeg signals using power spectral entropy.” IEEE, 2 2008, pp. 435–439.
  * [169] S. Babeetha and S. S. Sridhar, _EEG Signal Feature Extraction Using Principal Component Analysis and Power Spectral Entropy for Multiclass Emotion Prediction_ , 2023, pp. 435–448.
  * [170] D. Konar, S. De, P. Mukherjee, and A. H. Roy, “A novel human stress level detection technique using eeg.” IEEE, 2 2023, pp. 1–6.
  * [171] I. Shaer and A. Shami, “Sound event classification in an industrial environment: Pipe leakage detection use case,” in _2022 International Wireless Communications and Mobile Computing (IWCMC)_ , 2022, pp. 1212–1217.
  * [172] G. R. D, “Analysis of mfcc features for eeg signal classification,” _International Journal of Advances in Signal and Image Sciences_ , vol. 2, p. 14, 12 2016.
  * [173] M. Deng, T. Meng, J. Cao, S. Wang, J. Zhang, and H. Fan, “Heart sound classification based on improved mfcc features and convolutional recurrent neural networks,” _Neural Networks_ , vol. 130, pp. 22–32, 10 2020.
  * [174] Y. Arpitha, G. L. Madhumathi, and N. Balaji, “Spectrogram analysis of ecg signal and classification efficiency using mfcc feature extraction technique,” _Journal of Ambient Intelligence and Humanized Computing_ , vol. 13, pp. 757–767, 2 2022.
  * [175] M. Boussaa, I. Atouf, M. Atibi, and A. Bennis, “Ecg signals classification using mfcc coefficients and ann classifier.” IEEE, 5 2016, pp. 480–484.
  * [176] S. A. A. Yusuf and R. Hidayat, “Mfcc feature extraction and knn classification in ecg signals.” IEEE, 9 2019, pp. 1–5.
  * [177] M. Mohan, P. Dhanalakshmi, and R. S. Kumar, “Speech emotion classification using ensemble models with mfcc,” _Procedia Computer Science_ , vol. 218, pp. 1857–1868, 2023.
  * [178] A. Abbaskhah, H. Sedighi, and H. Marvi, “Infant cry classification by mfcc feature extraction with mlp and cnn structures,” _Biomedical Signal Processing and Control_ , vol. 86, p. 105261, 9 2023.
  * [179] X. Mu and C.-H. Min, “Mfcc as features for speaker classification using machine learning.” IEEE, 6 2023, pp. 0566–0570.
  * [180] F. Alharbi, S. Luo, H. Zhang, K. Shaukat, G. Yang, C. A. Wheeler, and Z. Chen, “A brief review of acoustic and vibration signal-based fault detection for belt conveyor idlers using machine learning models,” _Sensors_ , vol. 23, p. 1902, 2 2023.
  * [181] F. Rustam, A. Ishaq, M. S. A. Hashmi, H. U. R. Siddiqui, L. A. D. López, J. C. Galán, and I. Ashraf, “Railway track fault detection using selective mfcc features from acoustic data,” _Sensors_ , vol. 23, p. 7018, 8 2023.
  * [182] Z. K. Abdul and A. K. Al-Talabani, “Mel frequency cepstral coefficient and its applications: A review,” _IEEE Access_ , vol. 10, pp. 122 136–122 158, 2022.
  * [183] A. P. Petropulu, “Higher-order spectra in biomedical signal processing,” _IFAC Proceedings Volumes_ , vol. 27, pp. 47–52, 3 1994.
  * [184] C. Zhu, T. Cao, L. Chen, X. Dai, Q. Ge, and X. Zhao, “High-order domain feature extraction technology for ocean acoustic observation signals: A review,” _IEEE Access_ , vol. 11, pp. 17 665–17 683, 2023.
  * [185] K. C. Chua, V. Chandran, U. R. Acharya, and C. M. Lim, “Application of higher order statistics/spectra in biomedical signals—a review,” _Medical Engineering and Physics_ , vol. 32, pp. 679–689, 9 2010.
  * [186] S. A. Hosseini, “A hybrid approach based on higher order spectra for clinical recognition of seizure and epilepsy using brain activity,” _Basic and Clinical Neuroscience Journal_ , vol. 8, pp. 479–492, 11 2017.
  * [187] E. B. Assi, L. Gagliano, S. Rihana, D. K. Nguyen, and M. Sawan, “Bispectrum features and multilayer perceptron classifier to enhance seizure prediction,” _Scientific Reports_ , vol. 8, p. 15491, 10 2018.
  * [188] K. Tan, W. Yan, L. Zhang, Q. Ling, and C. Xu, “Semi-supervised specific emitter identification based on bispectrum feature extraction cgan in multiple communication scenarios,” _IEEE Transactions on Aerospace and Electronic Systems_ , vol. 59, pp. 292–310, 2 2023.
  * [189] Y. Zhou, R. Zhou, C. Wang, X. Wang, Y. Yu, and X. Zhang, “A modulation recognition method based on bispectrum and ensemble learning.” IEEE, 9 2022, pp. 124–128.
  * [190] X. Li, M. Yu, Y. Liu, and X. Xu, “Feature extraction of underwater signals based on bispectrum estimation.” IEEE, 9 2011, pp. 1–4.
  * [191] Z. Dong, F. Lv, T. Wan, K. Jiang, X. Fang, and L. Zhang, “Radar signal modulation recognition based on bispectrum features and deep learning.” IEEE, 6 2021, pp. 63–67.
  * [192] Y. Liu, Y. Zhou, W. Xin, Y. He, and P. Fan, “Bispectrum analysis for feature extraction of pitting fault in wind turbine gearbox.” IEEE, 8 2010, pp. 1298–1301.
  * [193] D. G. Bhalke, C. B. R. Rao, and D. S. Bormane, “Musical instrument classification using higher order spectra.” IEEE, 2 2014, pp. 40–45.
  * [194] A. C. McCormick and A. K. Nandi, “Bispectral and trispectral features for machine condition diagnosis,” _IEE Proceedings - Vision, Image, and Signal Processing_ , vol. 146, p. 229, 1999.
  * [195] K. Muthuvel, L. P. Suresh, T. J. Alexander, and S. H. K. Veni, _Classification of ECG Signal Using Hybrid Feature Extraction and Neural Network Classifier_ , 2015, pp. 1537–1544.
  * [196] M. K, J. A. T, M. P, T. Thangam, and P. S. L, “Hybrid feature extraction technique for electrocardiograph arrhythmia signal classification.” IEEE, 8 2023, pp. 1518–1524.
  * [197] C. K. Kovach and M. A. Howard, “Decomposition of higher-order spectra for blind multiple-input deconvolution, pattern identification and separation,” _Signal Processing_ , vol. 165, pp. 357–379, 12 2019.
  * [198] M. K. Gourisaria, R. Agrawal, M. Sahni, and P. K. Singh, “Comparative analysis of audio classification with mfcc and stft features using machine learning techniques,” _Discover Internet of Things_ , vol. 4, p. 1, 1 2024.
  * [199] A.-C. Tsai, J.-J. Luh, and T.-T. Lin, “A novel stft-ranking feature of multi-channel emg for motion pattern recognition,” _Expert Systems with Applications_ , vol. 42, pp. 3327–3341, 5 2015.
  * [200] T. Huynh-The, Q.-V. Pham, T.-H. Vu, D. B. da Costa, and V.-P. Hoang, “Intelligent spectrum sensing with convnet for 5g and lte signals identification.” IEEE, 7 2023, pp. 140–144.
  * [201] J. Huang, B. Chen, B. Yao, and W. He, “Ecg arrhythmia classification using stft-based spectrogram and convolutional neural network,” _IEEE Access_ , vol. 7, pp. 92 871–92 880, 2019.
  * [202] Y. Hu, L. Wang, and W. Fu, “Eeg feature extraction of motor imagery based on wt and stft.” IEEE, 8 2018, pp. 83–88.
  * [203] O. K. Cura, G. C. Yilmaz, H. S. Ture, and A. Akan, “Deep time-frequency feature extraction for alzheimer’s dementia eeg classification.” IEEE, 10 2022, pp. 1–4.
  * [204] A. Buyya, T. Ogeti, G. Suhas, P. Kashapogula, and A. K. Panigrahy, “Arrhythmias classification by using stft-based spectrograms, transfer learning and concatenation of features.” IEEE, 5 2023, pp. 1–5.
  * [205] H. Liu, L. Li, and J. Ma, “Rolling bearing fault diagnosis based on stft-deep learning and sound signals,” _Shock and Vibration_ , vol. 2016, pp. 1–12, 2016.
  * [206] P. Ewert, B. Wicher, and T. Pajchrowski, “Application of the stft for detection of the rotor unbalance of a servo-drive system with an elastic interconnection,” _Electronics_ , vol. 13, p. 441, 1 2024.
  * [207] Y. Hao, C. Zhang, Y. Lu, L. Zhang, Z. Lei, and Z. Li, “A novel autoencoder modeling method for intelligent assessment of bearing health based on short-time fourier transform and ensemble strategy,” _Precision Engineering_ , vol. 85, pp. 89–101, 1 2024.
  * [208] H. Shayeste and B. M. Asl, “Automatic seizure detection based on gray level co-occurrence matrix of stft imaged-eeg,” _Biomedical Signal Processing and Control_ , vol. 79, p. 104109, 1 2023.
  * [209] Z. Suryady, A. W. A. Rahman, and D. Oktarina, “Human emotion classification based on phonocardiography signals (pcg),” 2024, p. 020002.
  * [210] N. Sharma, G. G, and R. S. Anand, “Epileptic seizure detection using stft based peak mean feature and support vector machine.” IEEE, 8 2021, pp. 1131–1136.
  * [211] H. Zehir, T. Hafs, S. Daas, and A. Nait-Ali, “An ecg biometric system based on empirical mode decomposition and hilbert-huang transform for improved feature extraction.” IEEE, 6 2023, pp. 1–4.
  * [212] L. Li, S. Wang, Y. Zhao, and F. Wang, “Fault diagnosis for single-phase grounding in distribution network based on hilbert-huang transform and siamese convolution neural network.” IEEE, 5 2023, pp. 3571–3576.
  * [213] P. Warule, S. P. Mishra, S. Deb, and D. Joshi, “Hilbert-huang transform-based time-frequency analysis of speech signals for the identification of common cold.” IEEE, 10 2023, pp. 876–880.
  * [214] Y. P. Bórnea, A. L. O. Vitor, M. F. Castoldi, A. Goedtel, and W. A. Souza, “Classification of bearing faults in induction motors with the hilbert-huang transform and feature selection.” IEEE, 8 2023, pp. 567–573.
  * [215] D. Walsh, S. Dev, and A. Nag, “Hilbert-huang-transform based features for accent classification of non-native english speakers.” IEEE, 6 2023, pp. 1–6.
  * [216] B. S. Munir, M. Reza, A. Trisetyarso, and B. S. Abbas, “Feature extraction using hilbert-huang transform for power system oscillation measurements.” IEEE, 10 2017, pp. 93–96.
  * [217] D. Du, J. Zhang, Y. Fang, and J. Tian, “Motor bearing fault diagnosis based on hilbert-huang transform and convolutional neural networks.” IEEE, 10 2022, pp. 1–5.
  * [218] D. H. Kisa, M. A. Ozdemir, O. Guren, and A. Akan, “Classification of hand gestures using semg signals and hilbert-huang transform.” IEEE, 8 2022, pp. 1293–1297.
  * [219] N. M. Bhiri, S. Ameur, I. Jegham, M. A. Mahjoub, and A. B. Khalifa, “Fisher-hht: A feature extraction approach for hand gesture recognition with a leap motion controller.” IEEE, 5 2022, pp. 1–6.
  * [220] J. Li, Z. Liang, Y. Qi, L. Li, G. Li, N. Zheng, and Z. Wang, “Feature extraction and state identification of transformer dc bias vibration based on hht-svm.” IEEE, 4 2022, pp. 746–750.
  * [221] J. Chen, H. Li, L. Ma, H. Bo, and X. Gao, “Application of eemd-hht method on eeg analysis for speech evoked emotion recognition.” IEEE, 8 2020, pp. 376–381.
  * [222] K. Cai, W. Cao, L. Aarniovuori, H. Pang, Y. Lin, and G. Li, “Classification of power quality disturbances using wigner-ville distribution and deep convolutional neural networks,” _IEEE Access_ , vol. 7, pp. 119 099–119 109, 2019.
  * [223] M. Zulfiqar, M. F. U. Butt, A. Rama, and I. Shafi, “Abnormality detection in cardiac signals using pseudo wigner-ville distribution with pre-trained convolutional neural network.” IEEE, 12 2019, pp. 1–5.
  * [224] G. Wei, T. Jiang, Y. Liu, and W. Liu, “Dynamic gesture recognition using software defined radio based on smooth pseudo wigner-ville distribution.” IEEE, 12 2015, pp. 1–5.
  * [225] F. Akdeniz, I. Kayikcioglu, I. Kaya, and T. Kayikcioglu, “Using wigner-ville distribution in ecg arrhythmia detection for telemedicine applications.” IEEE, 6 2016, pp. 409–412.
  * [226] R. Abayneh, M. Mutala, J. Ren, and X. Yang, “Efficient wi-fi device rf fingerprint detection and classification using wigner-ville distribution.” IEEE, 11 2023, pp. 504–508.
  * [227] S. Taran, S. K. Khare, P. V. K. Krishna, and V. S. Kardam, _Focal and non-focal EEG signal classification using the Wigner–Ville distribution and deep feature extraction_. IOP Publishing, 2 2024, pp. 2–1–2–14.
  * [228] K. Kumar, P. Kumar, R. K. Patel, M. Sharma, V. Bajaj, and U. R. Acharya, “Time frequency distribution and deep neural network for automated identification of insomnia using single channel eeg-signals,” _IEEE Latin America Transactions_ , vol. 22, pp. 186–194, 3 2024.
  * [229] X. Zou, H. Mu, R. Wang, K. Fan, Z. Cheng, Y. He, and G. Zhang, “An efficient accuracy improvement method for cable defect location based on instantaneous filtering in time-frequency domain,” _Measurement_ , vol. 226, p. 114178, 2 2024.
  * [230] S. K. Dash and G. S. Rao, “Arrhythmia detection using wigner-ville distribution based neural network,” _Procedia Computer Science_ , vol. 85, pp. 806–811, 2016.
  * [231] P. Shegokar and P. Sircar, “Continuous wavelet transform based speech emotion recognition.” IEEE, 12 2016, pp. 1–8.
  * [232] C. Peng, W. Cheng, Z. Song, and R. Dong, “A noise-robust modulation signal classification method based on continuous wavelet transform.” IEEE, 6 2020, pp. 745–750.
  * [233] R. N. Toma, F. H. Toma, and J.-M. Kim, “Comparative analysis of continuous wavelet transforms on vibration signal in bearing fault diagnosis of induction motor.” IEEE, 9 2021, pp. 1–4.
  * [234] A. Belkhou, A. Achmamad, and A. Jbari, “Classification and diagnosis of myopathy emg signals using the continuous wavelet transform.” IEEE, 4 2019, pp. 1–4.
  * [235] R. Singh, S. Gangwar, S. Bartwal, and V. Tomar, “Wavelet-based feature extraction and rcnn for ecg signal classification.” IEEE, 6 2023, pp. 1–6.
  * [236] J. Fu, X. Xu, and Y. Chen, “Feature selection and optimization method based on cwt.” IEEE, 10 2017, pp. 1–4.
  * [237] N. A. Aditiya, Z. Darojah, D. R. Sanggar, and M. R. Dharmawan, “Fault diagnosis system of rotating machines using continuous wavelet transform and artificial neural network.” IEEE, 9 2017, pp. 173–176.
  * [238] S. Tang, B. C. Khoo, Y. Zhu, K. M. Lim, and S. Yuan, “A light deep adaptive framework toward fault diagnosis of a hydraulic piston pump,” _Applied Acoustics_ , vol. 217, p. 109807, 2 2024.
  * [239] J. Dong, H. Jiang, D. Su, Y. Gao, T. Chen, and K. Sheng, “Transfer learning rolling bearing fault diagnosis model based on deep feature decomposition and class-level alignment,” _Measurement Science and Technology_ , vol. 35, p. 046006, 4 2024.
  * [240] C. Bhagavatula, S. Venugopalan, R. Blue, R. Friedman, M. O. Griofa, M. Savvides, and B. V. K. V. Kumar, “Biometric identification of cardiosynchronous waveforms utilizing person specific continuous and discrete wavelet transform features.” IEEE, 8 2012, pp. 4311–4314.
  * [241] O. Almanza-Conejo, D. L. Almanza-Ojeda, J. L. Contreras-Hernandez, and M. A. Ibarra-Manzano, “Emotion recognition in eeg signals using the continuous wavelet transform and cnns,” _Neural Computing and Applications_ , vol. 35, pp. 1409–1422, 1 2023.
  * [242] R. Dwyer, “Detection of non-gaussian signals by frequency domain kurtosis estimation.” Institute of Electrical and Electronics Engineers, pp. 607–610.
  * [243] J. Antoni, “The spectral kurtosis: a useful tool for characterising non-stationary signals,” _Mechanical Systems and Signal Processing_ , vol. 20, pp. 282–307, 2 2006.
  * [244] Y. Wang, J. Xiang, R. Markert, and M. Liang, “Spectral kurtosis for fault detection, diagnosis and prognostics of rotating machines: A review with applications,” _Mechanical Systems and Signal Processing_ , vol. 66-67, pp. 679–698, 1 2016.
  * [245] S. Liu, S. Hou, K. He, and W. Yang, “L-kurtosis and its application for fault detection of rolling element bearings,” _Measurement_ , vol. 116, pp. 523–532, 2 2018.
  * [246] J. Wodecki, “Time-varying spectral kurtosis: Generalization of spectral kurtosis for local damage detection in rotating machines under time-varying operating conditions,” _Sensors_ , vol. 21, p. 3590, 5 2021.
  * [247] I. Ahmad, C. Yao, L. Li, Y. Chen, Z. Liu, I. Ullah, M. Shabaz, X. Wang, K. Huang, G. Li, G. Zhao, O. W. Samuel, and S. Chen, “An efficient feature selection and explainable classification method for eeg-based epileptic seizure detection,” _Journal of Information Security and Applications_ , vol. 80, p. 103654, 2 2024.
  * [248] Y. Liu, F. Yu, and J. Gao, “Sparse representation-based classification for rolling bearing fault diagnosis.” IEEE, 11 2019, pp. 3058–3061.
  * [249] J. C. Chan, H. Ma, and T. K. Saha, “Partial discharge pattern recognition using multiscale feature extraction and support vector machine.” IEEE, 2013, pp. 1–5.
  * [250] S. Sekkate, M. Khalil, and A. Adib, “Fusing wavelet and short-term features for speaker identification in noisy environment.” IEEE, 4 2018, pp. 1–8.
  * [251] M. Tibdewal, H. Dey, M. Mahadevappa, A. Ray, and M. Malokar, “Wavelet transform based multiple features extraction for detection of epileptic/ non-epileptic multichannel eeg.” IEEE, 2016, pp. 1648–1653.
  * [252] Y. Xie and T. Zhang, “Feature extraction based on dwt and cnn for rotating machinery fault diagnosis.” IEEE, 5 2017, pp. 3861–3866.
  * [253] F. J. Floresca, C. K. Tobias, and C. Ostia, “Naïve bayes classification technique for brushless dc motor fault diagnosis with discrete wavelet transform feature extraction.” IEEE, 3 2022, pp. 140–144.
  * [254] S. Katiyar and I. Sharma, “Emg signal decomposition methods for physical actions: A comparative analysis.” IEEE, 9 2023, pp. 1–5.
  * [255] C. M. Ugwu, C. P. Mukamakuza, and E. Tuyishimire, “Ecg-signals-based heartbeat classification: A comparative study of artificial neural network and support vector machine classifiers.” IEEE, 1 2024, pp. 000 217–000 222.
  * [256] S. Guo, S. Lin, and Z. Huang, “Feature extraction of p300s in eeg signal with discrete wavelet transform and fisher criterion.” IEEE, 10 2015, pp. 200–204.
  * [257] H. U. Amin, A. S. Malik, R. F. Ahmad, N. Badruddin, N. Kamel, M. Hussain, and W.-T. Chooi, “Feature extraction and classification for eeg signals using wavelet transform and machine learning techniques,” _Australasian Physical and Engineering Sciences in Medicine_ , vol. 38, pp. 139–149, 3 2015.
  * [258] A. Prochazka, J. Kukal, and O. Vysata, “Wavelet transform use for feature extraction and eeg signal segments classification.” IEEE, 3 2008, pp. 719–722.
  * [259] Q. Zhao and L. Zhang, “Ecg feature extraction and classification using wavelet transform and support vector machines.” IEEE, pp. 1089–1092.
  * [260] S. Y. Shah, H. Larijani, R. M. Gibson, and D. Liarokapis, “Epileptic seizure classification based on random neural networks using discrete wavelet transform for electroencephalogram signal decomposition,” _Applied Sciences_ , vol. 14, p. 599, 1 2024.
  * [261] Q. Gong, K. Peng, Q. Gao, L. Feng, and C. Xiao, “Series arc fault identification method based on wavelet transform and feature values decomposition fusion dnn,” _Electric Power Systems Research_ , vol. 221, p. 109391, 8 2023.
  * [262] J. Xi and L. Lin, “Multidimensional feature extraction based on vibration signals of rolling bearings.” IEEE, 5 2013, pp. 1093–1096.
  * [263] L.-Y. Zhao, L. Wang, and R.-Q. Yan, “Rolling bearing fault diagnosis based on wavelet packet decomposition and multi-scale permutation entropy,” _Entropy_ , vol. 17, pp. 6447–6461, 9 2015.
  * [264] M. J. Gómez, P. Marklund, D. Strombergsson, C. Castejón, and J. C. García-Prada, “Analysis of vibration signals of drivetrain failures in wind turbines for condition monitoring,” _Experimental Techniques_ , vol. 45, pp. 1–12, 2 2021.
  * [265] X. Ding, L. Lin, D. He, L. Wang, W. Huang, and Y. Shao, “A weight multinet architecture for bearing fault classification under complex speed conditions,” _IEEE Transactions on Instrumentation and Measurement_ , vol. 70, pp. 1–11, 2021.
  * [266] I. Attoui, N. Boutasseta, N. Fergani, B. Oudjani, and A. Deliou, “Vibration-based bearing fault diagnosis by an integrated dwt-fft approach and an adaptive neuro-fuzzy inference system.” IEEE, 5 2015, pp. 1–6.
  * [267] S. Aburakhia and A. Shami, “Sb-pdm: A tool for predictive maintenance of rolling bearings based on limited labeled data,” _Software Impacts_ , vol. 16, p. 100503, 5 2023.
  * [268] Z. Mezni, C. Delpha, D. Diallo, and A. Braham, “A comparative study for ball bearing fault classification using kernel-svm with kullback leibler divergence selected features.” IEEE, 10 2019, pp. 6969–6974.
  * [269] F. Wang, G. Deng, C. Liu, W. Su, Q. Han, and H. Li, “A deep feature extraction method for bearing fault diagnosis based on empirical mode decomposition and kernel function,” _Advances in Mechanical Engineering_ , vol. 10, p. 168781401879825, 9 2018.
  * [270] J. Shen, X. Zhang, G. Wang, Z. Ding, and B. Hu, “An improved empirical mode decomposition of electroencephalogram signals for depression detection,” _IEEE Transactions on Affective Computing_ , vol. 13, pp. 262–271, 1 2022.
  * [271] L. Zhan, F. Ma, J. Zhang, C. Li, Z. Li, and T. Wang, “Fault feature extraction and diagnosis of rolling bearings based on enhanced complementary empirical mode decomposition with adaptive noise and statistical time-domain features,” _Sensors_ , vol. 19, p. 4047, 9 2019.
  * [272] A. Ahmed, Y. Serrestou, K. Raoof, and J.-F. Diouris, “Empirical mode decomposition-based feature extraction for environmental sound classification,” _Sensors_ , vol. 22, p. 7717, 10 2022.
  * [273] H. Shang, K. Lo, and F. Li, “Partial discharge feature extraction based on ensemble empirical mode decomposition and sample entropy,” _Entropy_ , vol. 19, p. 439, 8 2017.
  * [274] S. Nalband, A. Prince, and A. Agrawal, “Entropy‐based feature extraction and classification of vibroarthographic signal using complete ensemble empirical mode decomposition with adaptive noise,” _IET Science, Measurement and Technology_ , vol. 12, pp. 350–359, 5 2018.
  * [275] M. Van and H. Kang, “Bearing‐fault diagnosis using non‐local means algorithm and empirical mode decomposition‐based feature extraction and two‐stage feature selection,” _IET Science, Measurement and Technology_ , vol. 9, pp. 671–680, 9 2015.
  * [276] Y. Li, J. hao Luo, Q. yun Dai, J. K. Eshraghian, B. W.-K. Ling, C. yan Zheng, and X. li Wang, “A deep learning approach to cardiovascular disease classification using empirical mode decomposition for ecg feature extraction,” _Biomedical Signal Processing and Control_ , vol. 79, p. 104188, 1 2023.
  * [277] N. M. El-Kafrawy, D. Hegazy, and M. F. Tolba, _Features Extraction and Classification of EEG Signals Using Empirical Mode Decomposition and Support Vector Machine_ , 2014, pp. 189–198.
  * [278] R. Jia, F. Ma, H. Wu, X. Luo, and X. Ma, “Coupling fault feature extraction method based on bivariate empirical mode decomposition and full spectrum for rotating machinery,” _Mathematical Problems in Engineering_ , vol. 2018, pp. 1–10, 2018.
  * [279] H. Yang, T. Ning, B. Zhang, X. Yin, and Z. Gao, “An adaptive denoising fault feature extraction method based on ensemble empirical mode decomposition and the correlation coefficient,” _Advances in Mechanical Engineering_ , vol. 9, p. 168781401769644, 4 2017.
  * [280] A. Mert, “Ecg feature extraction based on the bandwidth properties of variational mode decomposition,” _Physiological Measurement_ , vol. 37, pp. 530–543, 4 2016.
  * [281] P. K. Sahu and R. N. Rai, “Fault diagnosis of rolling bearing based on an improved denoising technique using complete ensemble empirical mode decomposition and adaptive thresholding method,” _Journal of Vibration Engineering and Technologies_ , vol. 11, pp. 513–535, 2 2023.
  * [282] Y. Yang, H. Liu, L. Han, and P. Gao, “A feature extraction method using vmd and improved envelope spectrum entropy for rolling bearing fault diagnosis,” _IEEE Sensors Journal_ , vol. 23, pp. 3848–3858, 2 2023.
  * [283] P. Poludasu, S. J. Bandaru, A. K. Paleru, S. Venkatadas, and P. A. K, “Biometric authentication using ecg signals.” IEEE, 5 2023, pp. 1–6.
  * [284] M. Feldman, “Hilbert transform in vibration analysis,” _Mechanical Systems and Signal Processing_ , vol. 25, pp. 735–802, 4 2011.
  * [285] G. Soto and S. Torres, “Feature extraction based on circular summary statistics in ecg signal classification.” IEEE, 11 2009, pp. 142–144.
  * [286] M. An-bo, Z. Wei, H. Hao-hao, X. Xin-yu, and C. Fu-lei, “Incipient fault feature extraction of main bearing by iterative squared envelope analysis.” IEEE, 7 2017, pp. 1–6.
  * [287] C. Liu, J. Wang, L. Liang, B. Niu, and D. Liu, “Periodic impact feature extraction for bearings fault based on envelope correlation kurtosis of singular value components.” IEEE, 12 2022, pp. 359–363.
  * [288] L. Han, J. Yan, S. Fan, M. Xu, Z. Liu, Y. Geng, and C. Guan, “Feature extraction of uhf pd signals based on diode envelope detection and linear discriminant analysis.” IEEE, 10 2019, pp. 598–602.
  * [289] D. Chowdhury, M. Hasan, and M. Z. R. Khan, “Statistical features extraction from current envelopes for non- intrusive appliance load monitoring.” IEEE, 3 2020, pp. 1–5.
  * [290] P. Zuo-wei, A. Hong-wen, L. Shuang-yin, and L. Yi-bing, “Amplitude envelope analysis for feature extraction of power plant blower bearing failure.” IEEE, 5 2014, pp. 2821–2824.
  * [291] S. Marquez-Figueroa, Y. S. Shmaliy, and O. Ibarra-Manzano, “Removing artifacts and optimal features extraction from emg envelope.” IEEE, 7 2020, pp. 90–95.
  * [292] L. Zhou, F. Yang, Y. Zhang, and S. Hou, “Feature extraction and classification of partial discharge signal in gis based on hilbert transform.” IEEE, 10 2021, pp. 208–213.
  * [293] M. R. Mehrjou, N. Mariun, M. Karami, N. Misron, and M. A. M. Radzi, “Broken rotor bar detection in ls-pmsms based on statistical features analysis of start-up current envelope.” IEEE, 11 2015, pp. 1–6.
  * [294] T. Deghboudj, A. Tlemçani, and A. Derghal, “Identifying broken rotor bars in squirrel cage induction motors: Examination of statistical characteristics derived from start-up current envelope.” IEEE, 11 2023, pp. 1–7.
  * [295] D.-H. Lee, C. Hong, W.-B. Jeong, and S. Ahn, “Time–frequency envelope analysis for fault detection of rotating machinery signals with impulsive noise,” _Applied Sciences_ , vol. 11, p. 5373, 6 2021.
  * [296] S. Kim, D. An, and J.-H. Choi, “Diagnostics 101: A tutorial for fault diagnostics of rolling element bearing using envelope analysis in matlab,” _Applied Sciences_ , vol. 10, p. 7302, 10 2020.
  * [297] Q. Hu, A. Qin, Q. Zhang, J. He, and G. Sun, “Fault diagnosis based on weighted extreme learning machine with wavelet packet decomposition and kpca,” _IEEE Sensors Journal_ , vol. 18, pp. 8472–8483, 10 2018.
  * [298] L. E. Crooks, _Noise reduction techniques in electronic systems (2nd ed.), Henry W. Ott. Wiley‐Interscience, New York. 1988_ , 6 1989, vol. 10.
  * [299] K. E. Barner and G. R. Arce, _21 Order-statistic filtering and smoothing of time-series: Part II_ , 1998, pp. 555–602.
  * [300] Z. Hao, Z. Cui, S. Yue, and H. Wang, “Impulsive noise removal in multi-frequency phase sensitive demodulation for electrical impedance tomography.” IEEE, 5 2018, pp. 1–6.
  * [301] D. Malathi, P. Naveen, V. Sahasra, and S. Rithika, “Vlsi implementation of median filter for noise removal in emg signal.” IEEE, 3 2023, pp. 422–426.
  * [302] W. Wierzchowski and M. Pawelczyk, “Median filtering approach for active control of impulsive noise.” IEEE, 9 2014, pp. 322–326.
  * [303] T. Pander, “A suppression of an impulsive noise in ecg signal processing.” IEEE, pp. 596–599.
  * [304] J. Wang, J. Li, S. Yan, W. Shi, X. Yang, Y. Guo, and T. A. Gulliver, “A novel underwater acoustic signal denoising algorithm for gaussian/non-gaussian impulsive noise,” _IEEE Transactions on Vehicular Technology_ , vol. 70, pp. 429–445, 1 2021.
  * [305] P. B. Swamy, R. S. Hallikar, and M. U. Kumari, “Enhancement of speech signals corrupted by impulsive noise using wavelets and adaptive median filtering.” IEEE, 9 2013, pp. 1–6.
  * [306] G. Tan, S. Yan, and B. Yang, “Impulsive noise suppression and concatenated code for ofdm underwater acoustic communications.” IEEE, 10 2022, pp. 1–6.
  * [307] R. Chaturvedi and Y. Yadav, “Application of moving average filter in ecg denoising,” _World Academics Journal of Engineering Sciences_ , p. 2004, 2014.
  * [308] V. Pandey and V. K. Giri, “High frequency noise removal from ecg using moving average filters.” IEEE, 3 2016, pp. 191–195.
  * [309] A. K. Tanji, M. A. G. de Brito, M. G. Alves, R. C. Garcia, G.-L. Chen, and N. R. N. Ama, “Improved noise cancelling algorithm for electrocardiogram based on moving average adaptive filter,” _Electronics_ , vol. 10, p. 2366, 9 2021.
  * [310] S. K. Salih, S. A. Aljunid, S. M. Aljunid, and O. Maskon, “Adaptive filtering approach for denoising electrocardiogram signal using moving average filter,” _Journal of Medical Imaging and Health Informatics_ , vol. 5, pp. 1065–1069, 9 2015.
  * [311] Z. Shan, J. Yang, M. A. F. Sanjuán, C. Wu, and H. Liu, “A novel adaptive moving average method for signal denoising in strong noise background,” _The European Physical Journal Plus_ , vol. 137, p. 50, 1 2022.
  * [312] Y. Liu, B. Dang, Y. Li, H. Lin, and H. Ma, “Applications of savitzky-golay filter for seismic random noise reduction,” _Acta Geophysica_ , vol. 64, pp. 101–124, 2 2016.
  * [313] N. S. Haider, R. Periyasamy, D. Joshi, and B. K. Singh, “Savitzky-golay filter for denoising lung sound,” _Brazilian Archives of Biology and Technology_ , vol. 61, 2018.
  * [314] J. Seo, H. Ma, and T. K. Saha, “On savitzky–golay filtering for online condition monitoring of transformer on-load tap changer,” _IEEE Transactions on Power Delivery_ , vol. 33, pp. 1689–1698, 8 2018.
  * [315] A. S. Vaishnavi, T. Greeshma, R. P. Teja, T. Padma, and C. U. Kumari, “Noise removal from ecg signal using lms adaptive filter implementation in xilinx system generator.” IEEE, 5 2023, pp. 1488–1491.
  * [316] R. Shaddeli, N. Yazdanjue, S. Ebadollahi, M. M. Saberi, and B. Gill, “Noise removal from ecg signals by adaptive filter based on variable step size lms using evolutionary algorithms.” IEEE, 9 2021, pp. 1–7.
  * [317] A. Mirza, S. Kabir, S. Ayub, and S. A. sheikh, “Impulsive noise cancellation of ecg signal based on ssrls,” _Procedia Computer Science_ , vol. 62, pp. 196–202, 2015.
  * [318] S. Dixit and D. Nagaria, “Lms adaptive filters for noise cancellation: A review,” _International Journal of Electrical and Computer Engineering (IJECE)_ , vol. 7, p. 2520, 10 2017.
  * [319] S. Yadav, S. K. Saha, and R. Kar, “An application of the kalman filter for eeg/erp signal enhancement with the autoregressive realisation,” _Biomedical Signal Processing and Control_ , vol. 86, p. 105213, 9 2023.
  * [320] R. I. Alfian, A. Ma’arif, and S. Sunardi, “Noise reduction in the accelerometer and gyroscope sensor with the kalman filter algorithm,” _Journal of Robotics and Control (JRC)_ , vol. 2, 2021.