# F0-based Gammatone Filtering for Intelligibility Gain of Acoustic Noisy
Signals

A. Queiroz, , and R. Coelho The authors are with the Laboratory of Acoustic
Signal Processing (lasp.ime.eb.br), Military Institute of Engineering (IME),
Rio de Janeiro, Brazil (email: coelho@ime.eb.br). This work was partially
suported by the National Council for Scientific and Technological Development
(CNPq) 307866/2015 and Fundação de Amparo à Pesquisa do Estado do Rio de
Janeiro (FAPERJ) 203075/2016. This work is also supported by the Coordenação
de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Grant Code
001.

###### Abstract

This letter proposes a time-domain method to improve speech intelligibility in
noisy scenarios. In the proposed approach, a series of Gammatone filters are
adopted to detect the harmonic components of speech. The filters outputs are
amplified to emphasize the first harmonics, reducing the masking effects of
acoustic noises. The proposed GTF${}_{\text{F0}}$ solution and two baseline
techniques are examined considering four background noises with different non-
stationarity degrees. Three intelligibility measures (ESTOI, ESII and
ASII${{}_{\text{ST}}}$) are adopted for objective evaluation. The experiments
results show that the proposed scheme leads to expressive speech
intelligibility gain when compared to the competing approaches. Furthermore,
the PESQ and WSS objective scores demonstrate that the proposed technique also
provides interesting quality improvement.

###### Index Terms:

Non-stationary noises, Gammatone filtering, intelligibility improvement.

##  I Introduction

Acoustic noise masking effects of speech signals is still a key element for
intelligibility improvement research. This issue underlies many applications
such as speech syntesis, source localization, and speech and speaker
recognition. The reduction of noise distortion is a major challenge to improve
quality and intelligibility of speech signals. Speech enhancement methods have
been proposed to treat non-stationary acoustic noises [1, 2, 3], leading to
expressive quality results. However, the harmonic components of speech, such
as fundamental frequency (F0) and formants, are generally not considered in
such solutions. F0 estimation is an essential benefit for speech audition,
particularly in noisy environment. Thus, it is here considered as a potential
factor to achieve intelligibility gain.

Recently, time-domain adaptive solutions have been designed to deal with the
harmonics of the speech signal to reduce the noise effects. In [4], the
formant center frequencies from voiced segments of speech are shifted away
from the region of noise. This formant shifting procedure [5] simulates the
human strategy to provide a more audible signal in noisy environment, i.e.,
the Lombard effect [6]. Results showed that the Smoothed Shifting of Formants
for Voiced segments (SSFV) is able to improve the intelligibility of speech
signals in car noise environment. A different approach was proposed in [7],
where linear harmonic models are applied to represent the voiced segments as a
sum of sinusoids. Each voiced frame is reconstructed as a sum of harmonics
whose frequencies correspond to the speech F0 and its first integer multiples.
The amplitude and phase estimation filter [8] was applied with the harmonic
models (APES${}_{\text{HARM}}$) and led to improved signal-to-noise ratios
(SNR) of the reconstructed speech signals [7].

This letter proposes a new time-domain approach namely GTF${}_{\text{F0}}$ to
attain intelligibility gain for speech signals corrupted by acoustic noises.
In this solution, Gammatone filters are applied to decompose the voiced
segments of speech into a series of the harmonics components with center
frequencies defined by integer multiples of F0. The F0 values are estimated
directly from the target noisy speech signal using the HHT-Amp method [9]. The
filters outputs are amplified by a gain factor, which emphasizes the first
harmonics of the speech signal leading to intelligibility improvement. In the
proposed GTF${}_{\text{F0}}$, the F0 values are not modified since such change
would not contribute to an improved speech intelligibility [10]. Furthermore,
it requires no prior knowledge of the speech or noise statistics, which makes
GTF${}_{\text{F0}}$ suitable to any kind of noisy environment.

Extensive experiments are conducted to evaluate the proposed scheme for speech
intelligibility and quality improvement. For this purpose, four acoustic
noises with different non-stationarity degrees are used to corrupt the speech
signals considering SNR between -5 dB and 5 dB. The formant shifting approach
(SSFV) [4] and the technique based on harmonic models (APES${}_{\text{HARM}}$)
[7] are adopted as baseline. Three objective intelligibility measures are used
to compare the proposed and baseline techniques: ESTOI [11], ESII [12] and
ASII${{}_{\text{ST}}}$ [13]. PESQ [14], LLR [15] and WSS [16] are selected to
examine the speech quality. Results show that the proposed solution
outperforms the competing methods in terms of speech intelligibility and
quality scores.

##  II F0 Estimation in Non-Stationary Noisy Scenario

In urban environments, speech signals are usually distorted by acoustic
background noises. Particularly, the F0 estimation accuracy can be highly
affected by the presence of acoustic noises. This task may become even more
challenging when the background noise is non-stationary [9].

###  II-A Non-Stationarity of Noisy Speech Signals

The non-stationarity degrees of speech signals corrupted by acoustic noises
are here examined according to the Index of Non-Stationarity (INS) [17]. The
INS objectively compares the target signal with stationary references called
surrogates. For each window length $T_{h}$, a threshold $\gamma$ is defined
for the stationarity assumption considering a confidence degree of $95\%$.
Thus,

$\text{INS}\begin{cases}\leq\gamma,&\text{signal is stationary};\\\
>\gamma,&\text{signal is non-stationary}.\end{cases}$ (1)

Figure 1: Spectrogram and respective INS for (a) clean speech signal and two
noisy versions with (b) SSN and (c) Babble noises with SNR of 0 dB.

Fig. 1 illustrates the spectrogram and INS values obtained for a clean and two
noisy versions of the same speech signal. The INS is computed for different
time scales $T_{h}/T$, where $T$ refers to the total duration of the analyzed
signal. A speech shaped noise (SSN) [18] and a Babble noise [19] are used to
corrupt the speech signal with SNR of 0 dB. Note that the presence of acoustic
noises significantly changes the temporal and spectral structures of the
speech signal. These masking effects can modify the signal harmonic components
(F0 and formants). And thus, it may induce speech intelligibility or quality
degradation. Furthermore, the noise corruption considerably attenuates the
non-stationary behavior of the clean speech signal. For instance, the maximum
INS value changes from 450 with clean speech to around 150 when corrupted by
the Babble noise.

###  II-B HHT-Amp F0 Estimation

The HHT-Amp method applies the Hilbert-Huang transform (HHT) [20] to analyze
the target speech signal. Instead of using the instantaneous frequencies as in
[21, 22], the F0 is estimated from the instantaneous amplitude functions of
the target signal. Let $x(t)$ denote a speech signal divided into $Q$ short-
time frames $x_{q}(t),q=1,2,\ldots,Q$. The HHT-Amp method is summarized as
follows:

  1. 1.

Apply the ensemble empirical mode decomposition (EEMD) [23] to decompose the
sample sequence $x_{q}(t)$ into a series of intrinsic mode functions (IMF) and
a residual $r_{q}(t)$, $x_{q}(t)=\sum_{m=1}^{M}\mbox{IMF}_{m,q}(t)+r_{q}(t)$.

  2. 2.

Compute the instantaneous amplitude functions as
$A_{m,q}(t)=|Z_{m,q}(t)|,m=1,\ldots,M,$ where the analytic signals are defined
as $Z_{m,q}(t)=\mbox{IMF}_{m,q}(t)+j\,H\\{\mbox{IMF}_{m,q}(t)\\}$, and
$H\\{\mbox{IMF}_{m,q}(t)\\}$ refers to the Hilbert transform of
$\mbox{IMF}_{m,q}(t)$.

  3. 3.

Calculate the ACF $r_{m,q}(\tau)=\sum_{t}A_{m}(t)\,A_{m}(t+\tau)$ of the
amplitude functions $A_{m,q}(t),m=1,\ldots,M$.

  4. 4.

For each decomposition mode $m$, let $\tau_{0}$ be the lowest $\tau$ value
that correspond to an ACF peak, subject to
$\tau_{min}\leq\tau_{0}\leq\tau_{max}$. The restriction is applied according
to the range $[F_{min},F_{max}]$ of possible F0 values. The $m$-th pitch
candidate is defined as $\tau_{0}/{f_{s}}$, where $f_{s}$ refers to the
sampling rate.

  5. 5.

Apply the decision criterion defined in [9] to select the best pitch candidate
$\hat{T}_{0}$. The estimated F0 is given by $\hat{\text{F0}}=1/\hat{T}_{0}$.

In [9], it was shown that the HHT-Amp method achieves interesting results in
estimating the fundamental frequency of noisy speech signals. The HHT-Amp was
evaluated in a wide range of noisy scenarios, including five acoustic noises
with different non-stationarity degrees. It outperformed four competing
estimators in terms of gross error (GE) and mean absolute error (MAE).

##  III Proposed Gammatone Filter Method: GTF${}_{\text{F0}}$

Figure 2: Block diagram of the proposed Gammatone Filter method for speech
intelligibility gain.

The block diagram of the proposed GTF${}_{\text{F0}}$ method is illustrated in
Fig. 2. The target noisy signal $x(t)$ is first split into $Q$ overlapping
short-time frames $x_{q}(t),q=1,2,\ldots,Q$, with $50\%$ overlapping. Two
disjoint sets are formed after the separation of voiced and unvoiced (V/UV)
segments. $S_{v}$ is composed by frames that contain voiced speech, and
$S_{u}$ consists of the remaining segments, i.e., unvoiced speech and noise.
For each voiced frame $q\in S_{v}$, the HHT-Amp method [9] is applied to
estimate the F0 value from $x_{q}(t)$. A total of $L$ Gammatone filters, with
center frequencies set to
$\hat{\text{F0}},2\,\hat{\text{F0}},\ldots,L\,\hat{\text{F0}}$, are used to
filter the sample sequence $x_{q}(t)$. Gain factors are employed to amplify
the filters outputs before the reconstruction of the speech frame
$\hat{x}_{q}(t)$. Finally, the overlap and add method is applied to all frames
to achieve the reconstructed version $\hat{x}(t)$ of the target speech signal.

###  III-A Gammatone Filtering

The Gammatone filter was introduced in [24] to describe the impulse response
of the auditory system. The time-domain impulse response of the Gammatone
filter is defined as

$g(t)=at^{n-1}\cos(2\pi f_{c}t+\phi)e^{-2\pi bt}\,,\,t\geq 0\,,$ (2)

where $a$ is the amplitude, $n$ is the filter order, $f_{c}$ is the center
frequency, $\phi$ is the phase, and $b$ is the bandwidth. In [25], it was
shown that a set of fourth-order Gammatone filters are able to represent the
magnitude characteristic of the human auditory system. In the Gammatone
auditory filterbank, the bandwidth $b$ presented in (2) is similar to the
Equivalent Rectangular Bandwidth (ERB) derived in [26], i.e.,
$b=1.019\,\text{ERB}$.

In the proposed GTF${}_{\text{F0}}$ method, a set of $L$ Gammatone filters
$\left\\{h_{k}(t),k=1\ldots,L\right\\}$ are applied to successively filter the
input sample sequence $x_{q}(t)$. Each filter $h_{k}(t)$ is implemented111Code
available at http://staffwww.dcs.shef.ac.uk/people/N.Ma/ considering order
$n=4$, center frequency $f_{c}=k\,\hat{\text{F0}}$, and bandwidth
$b=0.25\,\hat{\text{F0}}$. In order to align the impulse response functions,
phase compensation is applied to all filters, which correspond to the non-
causal filters

$h_{k}(t)=a(t+t_{c})^{n-1}\cos(2\pi f_{c}t)e^{-2\pi b(t+t_{c})}\,,\,t\geq-
t_{c}\,,$ (3)

where $t_{c}=\frac{n-1}{2\pi b}$ ensures that peaks of all filters occur at
$t=0$.

Let $x_{q}^{0}(t)=x_{q}(t)$, the filtered signals $y_{q}^{k}(t),k=1,\ldots,L$,
are recursively computed by

$\left\\{\begin{array}[]{l}y_{q}^{k}(t)=x_{q}^{k-1}(t)*h_{k}(t)\vspace{0.2cm}\\\
x_{q}^{k}(t)=x_{q}^{k-1}(t)-y_{q}^{k}(t)\end{array}\right.,\quad
k=1,\ldots,L\,.$ (4)

The residual signal is defined as $r_{q}(t)=x_{q}^{L}(t)$ to guarantee the
completeness of the input sequence. It means that
$x_{q}(t)=\sum_{k=1}^{L}y_{q}^{k}(t)+r_{q}(t)$.

Figure 3: Spectrogram of (a) a clean speech segment, the same signal corrupted
with (b) SSN and (c) Cafeteria noise with SNR of 0 dB, and (d-e) the
corresponding signals processed with the proposed GTF${}_{\text{F0}}$ method.

###  III-B Speech Signal Reconstruction

After the Gammatone filtering, the amplitude of the output samples
$y_{q}^{k}(t),k=1,\ldots,L$, are amplified by a factor $G_{k}\geq 1$. The idea
is to emphasize the presence of the first harmonics of the fundamental
frequency. This will induce speech intelligibility improvement without
introducing any noticeable distortion to the speech signal. The reconstruction
of the voiced frame $q\in S_{v}$ leads to the sample sequence

$\hat{x}_{q}(t)=\left[\sum_{k=1}^{L}G_{k}\,y_{q}^{k}(t)\right]+r_{q}(t)\,.$
(5)

For the reconstruction of the entire speech signal, the voiced frames obtained
in (5) and all the remaining frames in $S_{u}$ are joined together keeping the
original frames indices. Thus, all frames are overlap and added to reconstruct
the modified version $\hat{x}(t)$ of the target speech signal. The
completeness and continuity of $\hat{x}(t)$ is guaranteed by the adoption of
the Hanning window that multiply all frames before the overlap and add method.
This means that the reconstructed signal $\hat{x}(t)$ and the original signal
$x(t)$ would be exactly the same if $G_{k}=1$ for every
$k\in\left\\{1,\ldots,L\right\\}$.

Table I:  ESTOI, ESII, and ASII${}_{\text{ST}}$ measures [%] for UNP speech signals | ESTOI |  | ESII |  | ASII${}_{\text{ST}}$
---|---|---|---|---|---
SNR (dB) | -5 | -3 | 0 | 3 | 5 |  | -5 | -3 | 0 | 3 | 5 |  | -5 | -3 | 0 | 3 | 5
Babble | 0.28 | 0.33 | 0.40 | 0.48 | 0.53 |  | 0.34 | 0.38 | 0.44 | 0.50 | 0.54 |  | 0.38 | 0.40 | 0.45 | 0.50 | 0.54
Cafeteria | 0.30 | 0.35 | 0.43 | 0.51 | 0.57 |  | 0.36 | 0.39 | 0.45 | 0.52 | 0.56 |  | 0.39 | 0.41 | 0.46 | 0.51 | 0.55
SSN | 0.28 | 0.33 | 0.40 | 0.47 | 0.53 |  | 0.31 | 0.34 | 0.40 | 0.46 | 0.50 |  | 0.35 | 0.37 | 0.42 | 0.47 | 0.50
Volvo | 0.71 | 0.74 | 0.79 | 0.83 | 0.86 |  | 0.82 | 0.85 | 0.89 | 0.92 | 0.94 |  | 0.77 | 0.80 | 0.84 | 0.87 | 0.89

Fig. 3 illustrates an example application of the proposed GTF${}_{\text{F0}}$
to a speech signal selected from the TIMIT database [27]. The spectrogram of a
clean speech segment and two noisy versions are depicted in Figs. 3(a-c). The
corrupted signals are obtained with the SSN and Cafeteria222Available at
www.freesound.org. noises considering SNR of 0 dB. It can be noted that the
presence of the acoustic noises clearly induce the F0 harmonics to blur,
especially the first and second ones. The GTF${}_{\text{F0}}$ method
considering fixed gain of 3 dB to the first $L=5$ harmonics is applied to
these noisy signals. The resulting spectrograms are shown in Figs. 3(d-e).
Note that for both noises the GTF${}_{\text{F0}}$ method achieves more clearly
distinguished harmonics when compared to the noisy signals. This effect may
reduce the impact of the acoustic noise to speech intelligibility.

Table II: PESQ objective scores for noisy conditions at different SNRs | Babble |  | Cafeteria |  | SSN |  | Volvo |  | Overall
---|---|---|---|---|---|---|---|---|---
SNR (dB) | -5 | -3 | 0 | 3 | 5 |  | -5 | -3 | 0 | 3 | 5 |  | -5 | -3 | 0 | 3 | 5 |  | -5 | -3 | 0 | 3 | 5 |  | Average
UNP | 1.98 | 2.14 | 2.41 | 2.71 | 2.90 |  | 2.15 | 2.33 | 2.59 | 2.89 | 3.05 |  | 1.91 | 2.07 | 2.34 | 2.64 | 2.84 |  | 3.75 | 3.89 | 4.08 | 4.25 | 4.35 |  | 2.86
GTF${}_{\text{F0}}$ | 2.17 | 2.36 | 2.66 | 2.94 | 3.12 |  | 2.39 | 2.58 | 2.86 | 3.13 | 3.30 |  | 2.10 | 2.30 | 2.61 | 2.89 | 3.08 |  | 3.83 | 3.93 | 4.06 | 4.17 | 4.23 |  | 3.04
SSFV | 1.98 | 2.14 | 2.42 | 2.71 | 2.90 |  | 2.17 | 2.33 | 2.59 | 2.87 | 3.05 |  | 1.93 | 2.08 | 2.35 | 2.64 | 2.84 |  | 3.73 | 3.87 | 4.05 | 4.22 | 4.31 |  | 2.86
APES${}_{\text{HARM}}$ | 2.01 | 2.18 | 2.47 | 2.75 | 2.91 |  | 2.17 | 2.35 | 2.62 | 2.89 | 3.05 |  | 1.95 | 2.14 | 2.44 | 2.72 | 2.90 |  | 3.36 | 3.47 | 3.64 | 3.77 | 3.84 |  | 2.78

##  IV Experiments and Results

Several evaluation experiments are conducted with a subset of the TIMIT speech
database [27]. This is composed of 192 speech signals sampled at 16 kHz,
spoken by 24 speakers (16 male and 8 female). Each speech segment has an
average duration of 3 s. Four acoustic noises are applied for the speech
signals corruption. The SSN and Cafeteria noises are selected from the DEMAND
[18] and Freesound.org databases, respectively. Moreover, Babble and Volvo
noises are collected from the RSG-10 [19] database.

The proposed GTF${}_{\text{F0}}$ is implemented considering frames of 32 ms
and Gammatone filters bandwidth $b=0.25\,\hat{\text{F0}}$. The first $L=4$
harmonics are amplified considering the following gain factors:
$G_{1}=G_{2}=5.0$ dB, $G_{3}=4.0$ dB, and $G_{4}=2.5$ dB. The baseline formant
shifting approach (SSFV) considers the formant modification function that led
to the best results in [5]. The harmonic models solution with the APES filter
(APES${}_{\text{HARM}}$) is applied as described in [7].

###  IV-A Objective Intelligibility Evaluation

Figure 4: (a) $\Delta$ESTOI, (b) $\Delta$ESII, and (c)
$\Delta$ASII${}_{\text{ST}}$ intelligibility improvement [${\times 10^{-2}}$]
in four noisy conditions.

Tab. I presents the average ESTOI, ESII and ASII${}_{\text{ST}}$ scores
obtained with the noisy unprocessed (UNP) speech signals. The intelligibility
improvement achieved with the proposed and baseline solutions are depicted in
Fig. 4. Note from the ESTOI results that the GTF${}_{\text{F0}}$ leads to the
highest gain for all noisy scenarios. In average, it outperforms the SSFV
approach in 10% for the Babble, Cafeteria and SSN noises. For the highly non-
stationary Cafeteria noise, the proposed method attains an improvement of 10.1
at 0 dB, compared to 0.4 and -4.8 for the SSFV and APES${}_{\text{HARM}}$
techniques, respectively.

In terms of ESII and ASII${}_{\text{ST}}$ scores, it can be seen that the
GTF${}_{\text{F0}}$ leads to the best results for three noise sources: Babble,
Cafeteria and SSN. The only scenario where this solution does not achieve the
highest rates is the Volvo noise. In this case, all approaches lead to
negative intelligibility gain. It is due to the fact that the ESII and
ASII${}_{\text{ST}}$ scores for Volvo are higher than 0.77 for the noisy
signals (refer to Tab. I). The values are defined as very good intelligibility
[28, 29]. Among all the scenarios, GTF${}_{\text{F0}}$ accomplishes the
highest overall $\Delta$ESII and $\Delta$ASII${}_{\text{ST}}$ of 8.4 and 6.6,
respectively, for the non-stationary Babble noise with SNR of -3 dB. The
APES${}_{\text{HARM}}$ baseline method is outperformed by GTF${}_{\text{F0}}$
and SSFV in all scenarios.

###  IV-B Objective Quality Evaluation

The predicted quality scores computed with PESQ [14] are shown in Table II. As
it can be seen, GTF${}_{\text{F0}}$ attains the best PESQ results for three
background noise sources: Babble, Cafeteria and SSN. Considering the Volvo
noise, the unprocessed speech signals present good quality. It means that the
highest PESQ scores are obtained by UNP with SNR $\geq$ 0 dB. The
GTF${}_{\text{F0}}$ attains the best average PESQ value of 3.06, which is 0.17
greater than the noisy signals result.

The LLR [15] and WSS [16] measures are also adopted here to objectively
examine the speech signal in terms of quality. LLR scores are limited in the
range $[0,2]$, and just like WSS, smaller values indicate better quality. Fig.
5 shows the results as mean scores computed for the four noise sources at each
SNR. Note that the GTF${}_{\text{F0}}$ presents the smallest WSS values for
all SNR values. These results reinforce the capacity of the proposed solution
to emphasize the harmonic components of speech signals, providing improvement
in terms of both intelligibility and quality.

Figure 5: Mean LLR (top) and WSS (bottom) quality scores for Babble,
Cafeteria, SSN and Volvo noises.

##  V Conclusion

This letter introduced the time-domain GTF${}_{\text{F0}}$ method to improve
intelligibility and quality of speech signals. In this solution, F0 estimation
and Gammatone filtering are applied to emphasize the first harmonics of the
noisy speech signal. Four acoustic noises were considered to compose the
evaluation scenario. Six objective prediction measures were applied to examine
the proposed and competitive solutions. Results showed that
GTF${}_{\text{F0}}$ achieved the best intelligibility and quality scores
considering ESTOI and PESQ prediction measures for all acoustic noises.

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