# Blind Localization of Room Reflections with Application to Spatial Audio

1st Yogev Hadadi  Electrical and Computer Engineering
Ben-Gurion University of the Negev
Beer-Sheva 84105, Israel
<EMAIL_ADDRESS>2nd Vladimir Tourbabin  Reality Labs Research @ Meta
Redmond, WA USA
<EMAIL_ADDRESS>3rd Paul Calamia  Reality Labs Research @ Meta
Redmond, WA USA
<EMAIL_ADDRESS>4th Boaz Rafaely  Electrical and Computer Engineering
Ben-Gurion University of the Negev
Beer-Sheva 84105, Israel
<EMAIL_ADDRESS>
###### Abstract

Blind estimation of early room reflections, without knowledge of the room
impulse response, holds substantial value. The FF-PHALCOR (Frequency Focusing
PHase ALigned CORrelation) method was recently developed for this objective,
extending the original PHALCOR method from spherical to arbitrary arrays.
However, previous studies only compared the two methods under limited
conditions without presenting a comprehensive performance analysis. This study
presents an advance by evaluating the algorithm’s performance in a wider range
of conditions. Additionally, performance in terms of perception is
investigated through a listening test. This test involves synthesizing room
impulse responses from known room acoustics parameters and replacing the early
reflections with the estimated ones. The importance of the estimated
reflections for spatial perception is demonstrated through this test.

###### Index Terms:

Direction-of-arrival, Phase-Alignment, arbitrary array, early room
reflections, sparse recovery, spherical array

##  I Introduction

Numerous signal processing tasks such as optimal beamforming [1], room
geometry inference [2, 3], source separation [4], speech enhancement and
dereverberation [5], [6], may benefit from knowledge about early room
reflections. Furthermore, early reflections affect sound perception by
enhancing speech intelligibility, creating a feeling of listener envelopment,
and enabling the evaluation of source features such as width, loudness, and
distance [7], [8]. Hence, methods for the blind estimation of early
reflections have potential in applications of spatial audio signal
processing[9, 10, 11].

Methods for the blind estimation of room reflections have been previously
suggested. These include beamforming [2], MUSIC and ESPRIT [12, 13, 14, 15].
However, they presented an estimation of only a few reflections due to the
inherent limited spatial resolution of the array[16] and the density of
reflections in space and time. Recently, a method was proposed that overcame
the limitations of these previous methods. The method, named PHALCOR[17], used
a phase-aligned transform to decorrelate reflections along time and spatial
decomposition to separate them spatially. Finally, utilizing time-space
clustering, the method accurately estimated dozens of room reflections and
outperformed previous methods. However, this method was only developed and
investigated for spherical arrays using spherical harmonics signals. In
follow-up work, a more generalized method named FF-PHALCOR [18] was proposed
based on frequency focusing [19], extending the method to arbitrary arrays.
This recent study demonstrated that the method achieved performance comparable
to PHALCOR but explored only a limited set of conditions without presenting a
comprehensive analysis.

This study offers a more comprehensive investigation of the FF-PHALCOR
algorithm by evaluating the performance in a wider range of conditions.
Furthermore, the analysis extends to spatial perception, where a listening
test is conducted to examine the impact of estimating the Directions of
Arrival (DOAs) of early reflections on the reproduction of room impulse
responses (RIR) compared to synthesis based on a few room acoustics
parameters. While a spherical array is still used in this paper, the algorithm
operates directly on microphone signals and not in the spherical harmonics
domain, therefore, moving towards operating with arbitrary arrays.

The paper is structured as follows: Section II describes the system model, and
Section III describes the proposed algorithm. Next, Section IV presents the
results of a simulation study conducted to evaluate performance under various
acoustic conditions. Section V presents the results of the listening test.
Finally, the paper is concluded in Section VI.

##  II Signal Model

The acoustic scenario is a room consisting of a single source and a microphone
array with $Q$ microphones. The speech signal in the frequency domain ($f$) is
denoted by $\psi(f)$. The presence of $K$ early reflections is assumed,
considered attenuated and delayed replicas of the anechoic source signal [20].
The $k^{th}$ reflection is represented as a distinct source,
$\emph{s}_{k}(f)$, with a direction of arrival (DOA) $\Omega_{k}$, delay
$\tau_{k}$, and attenuation factor $\alpha_{k}$. $k=0$ represents the direct
sound with the DOA $\Omega_{0}$, and normalized parameters such that
$\tau_{0}=0$ and $\alpha_{0}=1$. Then:

$s_{k}(f)=\alpha_{k}e^{-i2\pi f\tau_{k}}\psi(f)$ (1)

The vector $\mathbf{s}(f):=[s_{0}(f),s_{1}(f),\dots,s_{K}(f)]^{T}$ represents
the concatenation of the direct sound and its $K$ early reflections arranged
in an ascending order of delay. The pressure captured at the microphone array
is represented by $\mathbf{p}(f):=[p_{1}(f),p_{2}(f),\dots,p_{Q}(f)]^{T}$
where each element corresponds to the pressure captured by a single
microphone, resulting in the following array equation:

$\mathbf{p}(f)=\mathbf{H}(f,\mathbf{\Omega})\mathbf{s}(f)+\mathbf{n}(f)$ (2)

$\mathbf{n}(f)$ includes the captured noise and the late reverberation, and
the steering matrix $\mathbf{H}(f,\mathbf{\Omega})$ is constructed as follows:

$\mathbf{H}(f,\mathbf{\Omega}):=[\mathbf{h}(f,\Omega_{0}),\dots,\mathbf{h}(f,\Omega_{K})]$
(3)

where each $\mathbf{h}(f,\Omega_{k})$ represents the steering vector in a free
field of the $k^{th}$ reflection. Then, a frequency-independent steering
matrix is obtained by employing frequency-focusing over the signal to apply
the Phase-Alignment transform.

##  III FF-PHALCOR Algorithm

The first stage of the algorithm is frequency focusing, required to equalize
the steering vectors within a selected band (with fixed bandwidth denoted by
$BW$) centered around the center frequency $f_{0}$. Then, for each frequency
$f$ within the band, a focusing matrix $\mathbf{T}(f,f_{0})$ is computed by
solving[19, 18]:

$\mathbf{T}(f,f_{0})\mathbf{H}(f,\mathbf{\Omega})=\mathbf{H}(f_{0},\mathbf{\Omega})$
(4)

where $\mathbf{H}(f_{0},\mathbf{\Omega})$ and $\mathbf{H}(f,\mathbf{\Omega})$
are constructed using equation (3). Applying focusing to equation (2) leads
to:

$\tilde{\mathbf{p}}(f)=\mathbf{T}(f,f_{0})\mathbf{p}(f)=\mathbf{H}(f_{0},\mathbf{\Omega})\mathbf{s}(f)+\mathbf{T}(f,f_{0})\mathbf{n}(f)$
(5)

After applying focusing, the spatial correlation matrix is computed:

$\mathbf{R}(f)=\mathbb{E}[\tilde{\mathbf{p}}(f)\tilde{\mathbf{p}}(f)^{H}]$ (6)

This matrix is usually dense in space and time, and to make it more sparse to
allow improved separation of reflections, the Phase-Alignment transform is
introduced as follows:

$\overline{\mathbf{R}}(\tau,f):=\sum_{j=0}^{J_{f}-1}\omega_{j}\mathbf{R}(f_{j})e^{i2\pi\tau
j\Delta f}$ (7)

The parameter $J_{f}$ represents the total frequency points, $\Delta f$ is the
frequency resolution, and $f_{j}=f+j\Delta f$. The weights
$\omega_{0},\dots,\omega_{J_{f}-1}$ are non-negative and inversely
proportional to $tr(\mathbf{R}(f_{j}))$. In the original work [17], it was
shown that taking $\tau=\tau_{k}-\tau_{k^{\prime}}$, with $k^{\prime}=0$ (the
direct sound) enhances entries in $\overline{\mathbf{R}}(\tau,f)$ which
corresponds to reflections with delay $\tau_{k}$. Truncating its singular-
value decomposition (SVD) provides a rank-1 approximation of
$\overline{\mathbf{R}}(\tau)$, denoted by $\overline{\mathbf{R}}_{1}(\tau)$.

$\overline{\mathbf{R}}_{1}(\tau)=\sigma_{\tau}\mathbf{u}_{\tau}\mathbf{v}_{\tau}^{H}$
(8)

For each $\tau$, the first singular value is denoted as $\sigma_{\tau}$, and
the left and right singular vectors are represented by $\mathbf{u}_{\tau}$ and
$\mathbf{v}_{\tau}$, respectively. It is shown that the former represents a
superposition of the steering vectors of reflection arriving at a similar
delay, while the latter represents the steering vector of the direct sound.
The final stage of the algorithm is detecting and clustering of estimated
delays and DOAs, performed using the DBSCAN algorithm [21], where identified
clusters represent reflections. Further algorithm details can be found in [17,
18].

##  IV Simulation Study

This study conducted a simulation to assess performance under various acoustic
conditions. In the following section, a listening test was carried out using
data from one of the simulated rooms.

###  IV-A Simulation Setup

The simulation setup involved shoe-box rooms with dimensions specified in
Table I, a speaker modeled as a point source, and a rigid spherical microphone
array with a radius of $4.2\,$cm consisting of $32\,$microphones, similar to
the Eigenmike [22]. The distance between the source and the array is also
detailed in the table. The Room Impulse Response (RIR) from the speaker to the
array was generated using the image method [20], while the speech signal used
in the simulation was a $2.5\,$second sample from the TSP Speech Database
[23], recorded at a sampling frequency of $48\,$kHz. The microphone signals
were generated using a sound field model of order $N=8$ in the spherical
harmonics domain, generated directly from the image source data [20, 24]. The
Direct to Reverberant Ratio (DRR) is calculated from the RIR as in Eq (1) in
[25], $T_{60}$ and critical distance are obtained by the diffuse model using
Sabine formula [26, 27, 28, 29] for each simulated room and scene, all
presented in the table.

TABLE I: Dimensions, $T_{60}$, Critical distance ($R_{c}$), source-array Distance and DRR of the simulated rooms and acoustic scenes Room | Dim $\left[m\right]^{3}$ | $\mathbf{T_{60}[s]}$ | $R_{c}$ [m] | Distance [m] | DRR [dB]
---|---|---|---|---|---
1 | [8,6,4] | 0.413 | 1.22 | 4.03 | -11.5
2 | [7,5,3] | 0.186 | 1.34 | 3.00 | -4.0
3 | [9,7,4] | 0.841 | 0.98 | 1.28 | -5.2
4 | [11,7,4] | 0.876 | 1.06 | 1.97 | -7.57
5 | [13,8,5] | 1.055 | 1.26 | 4.90 | -13.6

###  IV-B Methodology

First, a short-time Fourier transform (STFT) is computed for the microphone
signals $p_{q}$, using the Hanning window with a size of $150\,$ms,
$f_{s}=48\,$kHz sampling frequency, and an overlap of $75\%$. An operating
frequency range of $[500,5000]\,$Hz was selected, with a bandwidth of $2\,$kHz
for focusing, $J_{f}=8$ frequency bins was utilized for equation (7) [17].
Focusing is applied using a simulated steering matrix constructed with 900
DOAs sampled by the Fliege-Maier method [30]. Finally the hyper-parameters as
defined in the original paper[17] were selected as follows: $\rho_{min}=0.9$,
$\epsilon_{u}=0.63$, $\Omega_{th}=10^{\circ}$, $S_{max}=3$,
$\gamma_{\Omega}=8^{\circ}$ and $\gamma_{\tau}=0.3\,$ms, and the density
threshold is $0.15$.

For the performance evaluation, a reflection is classified as a true positive
if it matches a true reflection (obtained using the image method) within
specified tolerances set to $0.5\,$ms in delay, and $15^{\circ}$ in DOA. The
Probability of Detection (PD) is defined as follows:

$PD:=\frac{\\#\;true\;positive\;detections}{\\#reflections\;in\;the\;ground\;truth}$
(9)

The Probability of False Alarm (PFA) is defined as follows:

$PFA:=\frac{\\#\;false\;positive\;detections}{\\#detected\;reflections}$ (10)

###  IV-C Results

Fig. 1 presents the clustering of the algorithm in the first room. The axes
are the elevation angle $\theta$, the azimuth angle $\phi$ both in degrees,
and the delay $\tau$ in milliseconds. The pink circles are the ground truth
obtained from the image method. The colored regions are the results of the
clustering algorithm. A more detailed analysis of this result revealed that
the algorithm successfully detected the direct sound and 23 out of 28
reflections with $PD=82\%$ and $PFA=0$. As partially seen in this figure, the
algorithm better estimates sparser reflections compared to denser reflections
as the clustering algorithm may mistakenly group multiple reflections.

Table II displays the algorithm’s performance under various conditions. The
first column is the room number, corresponding to Table I, and the second
presents the number of reflections within $20\,$ms of the RIR. The third
column presents the number of reflections the algorithm detected, including
false alarms. Finally, the last columns present the PD and PFA calculated as
in equations ((9)) and ((10)). It can be seen that overall the algorithm
performs well and detects about $18-29$ reflections in each room $(1,2,5)$ and
$8-9$ in $3,4$.

TABLE II: Simulations results, where $\\#$Reflections is the number of reflections within the first 20ms of the RIR (including the direct sound), $\\#$Detections (including false-alarms). PD, PFA are also presented Room |  $\\#$Reflections |  $\\#$Detections** | PD | PFA
---|---|---|---|---
1 | 29 | 24 | $82\%$ | 0
2 | 38 | 29 | $52\%$ | $24\%$
3 | 9 | 9 | $100\%$ | 0
4 | 8 | 8 | $100\%$ | 0
5 | 16 | 18 | $94\%$ | $17\%$
Figure 1: Clustering of DOA, delay obtained in room1. $\tau$ [ms] is the
delay, $\theta$,$\phi$ [deg] are the elevation and the azimuth. The rings are
the ground truths.

##  V Listening Test

As demonstrated in the preceding section, the algorithm successfully detects
early reflections. It has been established [31, 11] that early reflections
play an important role in spatial perception. To evaluate the application of
FF-PHALCOR in the context of spatial perception, a listening test was
conducted based on the MUSHRA test (Multiple Stimuli with Hidden Reference and
Anchor) [32].

###  V-A Setup

The setup comprises a shoe-box room with the same dimensions as room 1 in
Table I. It includes a speaker located at $[5.5,1.2,1.7]$ and a $32$-channel
spherical microphone array located at $[2.5,3.9,1.7]$, with
$T_{60}=0.424\,$seconds, and DRR $=-11.5\,$dB. The signal is a $2.5\,$second
segment extracted from the TSP Speech Database [23]. The head-related transfer
function (HRTF) used in the experiment is derived from the Neumann
KU-$100$[33].

###  V-B Methodology

The test comprises three signals: the reference signal, a synthesized anchor
signal, and the estimated signal. The reference signal is generated by
applying the image method to compute the room impulse response with an order
of $N=40$.

The synthesized anchor signal was generated using known room acoustics
parameters: the room volume $V$, $T_{60}$, DRR, and DOA of the direct sound.
In this case, the room volume is $V=192\,m^{3}$, and the DOA of the direct
sound is given as $(90,-42.2)\,$degrees, the elevation and azimuth angle in
the range of $[0,\pi]\times[-\pi,\pi)$, respectively. Next, the expected
cumulative number of reflections was computed using a model based on the image
method [20], and this estimated number was used to generate reflection delays
in 5ms frames randomly. The amplitude of the reflections was selected to fit a
decay curve to achieve the desired $T_{60}$ value as calculated using the
Schroeder integral [34]. Reflections’ DOAs were randomly selected from a
uniform distribution over the sphere. The first reflection is considered as
the direct sound with a known DOA, and its amplitude is calculated to maintain
the DRR value.

For the estimated signal, the initial 20ms of the synthesized RIR described
above is replaced with the reflections estimated by the algorithm, keeping the
amplitudes the same as in the synthesized. Subsequently, all signals are
convolved with the head-related impulse response (HRIR) to create a binaural
room impulse responses (BRIR)[35]. Then, the speech signal is convolved with
the BRIR to generate the signals. Finally, the synthetic and estimated signals
were equalized in power to equal the reference. As a final stage, headphone
equalization was applied.

A total of 12 participants with normal hearing took part in the listening
test. The experiment consisted of a single MUSHRA screen, where all three
signals were played back using the audio player in MATLAB (MATLAB R2022b).
Participants were instructed to rate the overall quality on a scale from 0 to
100. Before rating, participants were given a training task to ensure
understanding of the instructions and familiarize themselves with the signals.

###  V-C Results

Fig. 2 displays the test results conducted in this study. The three Boxes
represent the evaluated signals, and the y-axis represents the similarity to
the reference signal. Furthermore, a Repeated Measures ANalysis of VAriance
(RMANOVA)[36] has been performed. In this test, one within-subject variables
was analyzed, i.e the reproduction method. The method variable exhibited a
statistically significant main effect, as revealed by the RM-ANOVA analysis, a
$F(2,22)=76.54$, $p<0.001$ and $\eta_{p}^{2}=0.874$. Given the statistically
significant main effect observed for the method variable, a post-hoc test was
conducted with Bonferroni correction to investigate this result further.
Pairwise comparisons were made between the estimated marginal means. The
reference and the estimated signals were not statistically significant, with a
mean difference of $7.583$ and $p=0.24$. However, the reference and the
synthesized signals and the estimated and the synthesized signals are
statistically significant with mean differences of $72.083,64.5$ respectively,
and $p<0.001$. This indicates that the algorithm successfully enhanced the
spatial perception by incorporating the knowledge of early room reflections.

These findings highlight the effectiveness of the FF-PHALCOR algorithm in
improving spatial perception by incorporating estimated early room reflections
into the reproduced signals.

Figure 2: The results of the overall quality test, in a box plot
visualization. The red line represents the median, the edges represent the
25th and 75th percentiles. The whiskers show the range of values excluding
outliers. Outliers are marked with a red ”+” symbol.

##  VI Conclusions

This paper showcases the effectiveness of the proposed algorithm in detecting
a significant number of reflections. Moreover, it demonstrates the impact of
the algorithm’s estimation of early reflections on sound perception. These
findings represent an advancements in the extension of the PHALCOR method to
arbitrary arrays.

For future work, it is recommended to study the algorithm’s performance over
non-spherical arrays, and to deepen the impact of the algorithm on the spatial
perception of reproduced signals.

## References

  * [1] H. A. Javed, A. H. Moore, and P. A. Naylor, “Spherical microphone array acoustic rake receivers,” in _2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)_. IEEE, 2016, pp. 111–115.
  * [2] E. Mabande, K. Kowalczyk, H. Sun, and W. Kellermann, “Room geometry inference based on spherical microphone array eigenbeam processing,” _The Journal of the Acoustical Society of America_ , vol. 134, no. 4, pp. 2773–2789, 2013.
  * [3] K. MacWilliam, F. Elvander, and T. v. Waterschoot, “Simultaneous acoustic echo sorting and 3-d room geometry inference,” in _ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)_ , 2023, pp. 1–5.
  * [4] E. Vincent, N. Bertin, R. Gribonval, and F. Bimbot, “From blind to guided audio source separation: How models and side information can improve the separation of sound,” _IEEE Signal Processing Magazine_ , vol. 31, no. 3, pp. 107–115, 2014.
  * [5] K. Kowalczyk, S. Kacprzak, and M. Ziółko, “On the extraction of early reflection signals for automatic speech recognition,” in _2017 IEEE 2nd International Conference on Signal and Image Processing (ICSIP)_. IEEE, 2017, pp. 351–355.
  * [6] Y. Peled and B. Rafaely, “Method for dereverberation and noise reduction using spherical microphone arrays,” in _2010 IEEE International Conference on Acoustics, Speech and Signal Processing_. IEEE, 2010, pp. 113–116.
  * [7] J. Catic, S. Santurette, and T. Dau, “The role of reverberation-related binaural cues in the externalization of speech,” _The Journal of the Acoustical Society of America_ , vol. 138, no. 2, pp. 1154–1167, 2015.
  * [8] M. Vorländer, _Auralization: Fundamentals of Acoustics, Modelling, Simulation, Algorithms and Acoustic Virtual Reality_. Springer Science & Business Media, 2007.
  * [9] V. Pulkki, S. Delikaris-Manias, and A. Politis, _Parametric time-frequency domain spatial audio_. Wiley Online Library, 2018.
  * [10] P. Coleman, A. Franck, P. Jackson, R. J. Hughes, L. Remaggi, F. Melchior _et al._ , “Object-based reverberation for spatial audio,” _Journal of the Audio Engineering Society_ , vol. 65, no. 1/2, pp. 66–77, 2017.
  * [11] B. Rafaely, V. Tourbabin, E. Habets, Z. Ben-Hur, H. Lee, H. Gamper, L. Arbel, L. Birnie, T. Abhayapala, and P. Samarasinghe, “Spatial audio signal processing for binaural reproduction of recorded acoustic scenes–review and challenges,” _Acta Acustica_ , vol. 6, p. 47, 2022.
  * [12] H. Sun, E. Mabande, K. Kowalczyk, and W. Kellermann, “Localization of distinct reflections in rooms using spherical microphone array eigenbeam processing,” _The Journal of the Acoustical Society of America_ , vol. 131, no. 4, pp. 2828–2840, 2012.
  * [13] B. Jo and J.-W. Choi, “Robust localization of early reflections in a room using semi real-valued EB-ESPRIT with three recurrence relations and laplacian constraint,” in _International Commission for Acoustics (ICA)_. International Commission for Acoustics (ICA), 2019.
  * [14] D. Ciuonzo, G. Romano, and R. Solimene, “Performance analysis of time-reversal music,” _IEEE Transactions on Signal Processing_ , vol. 63, no. 10, pp. 2650–2662, 2015.
  * [15] D. Ciuonzo, “On time-reversal imaging by statistical testing,” _IEEE Signal Processing Letters_ , vol. 24, no. 7, pp. 1024–1028, 2017.
  * [16] H. Kuttruff, _Room Acoustics_. Crc Press, 2016.
  * [17] T. Shlomo and B. Rafaely, “Blind localization of early room reflections using phase aligned spatial correlation,” _IEEE Transactions on Signal Processing_ , vol. 69, pp. 1213–1225, 2021.
  * [18] Y. Hadadi, V. Tourbabin, P. Calamia, and B. Rafaely, “Towards blind localization of room reflections with arbitrary microphone arrays,” _Journal of the Audio Engineering Society_ , august 2022.
  * [19] H. Beit-On and B. Rafaely, “Focusing and frequency smoothing for arbitrary arrays with application to speaker localization,” _IEEE/ACM Transactions on Audio, Speech, and Language Processing_ , vol. 28, pp. 2184–2193, 2020.
  * [20] J. B. Allen and D. A. Berkley, “Image method for efficiently simulating small-room acoustics,” _The Journal of the Acoustical Society of America_ , vol. 65, no. 4, pp. 943–950, 1979.
  * [21] M. Ester, H.-P. Kriegel, J. Sander, X. Xu _et al._ , “A density-based algorithm for discovering clusters in large spatial databases with noise.” in _Kdd_ , vol. 96, no. 34, 1996, pp. 226–231.
  * [22] M. H. Acoustics, “Em32 eigenmike microphone array release notes (v17. 0),” _25 Summit Ave, Summit, NJ 07901, USA_ , 2013.
  * [23] P. Kabal, “TSP speech database,” _McGill University, Database Version_ , vol. 1, no. 0, pp. 09–02, 2002.
  * [24] B. Rafaely, _Fundamentals of Spherical Array Processing_. Springer, 2015, vol. 8.
  * [25] P. Calamia, N. Balsam, and P. Robinson, “Blind estimation of the direct-to-reverberant ratio using a beta distribution fit to binaural coherence,” _The Journal of the Acoustical Society of America_ , vol. 148, no. 4, pp. EL359–EL364, 2020.
  * [26] W. C. Sabine and M. D. Egan, “Collected papers on acoustics,” 1994.
  * [27] H. Kuttruff and E. Mommertz, “Room acoustics,” in _Handbook of Engineering Acoustics_. Springer, 2012, pp. 239–267.
  * [28] W. C. Sabine, “Reverberation,” _The American Architect_ , vol. 4, 1900.
  * [29] L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, _Fundamentals of Acoustics_. John wiley & sons, 2000\.
  * [30] J. Fliege and U. Maier, “A two-stage approach for computing cubature formulae for the sphere,” in _Mathematik 139T, Universitat Dortmund, Fachbereich Mathematik, Universitat Dortmund, 44221_. Citeseer, 1996.
  * [31] S. Kitić and J. Daniel, “Blind identification of ambisonic reduced room impulse response,” _arXiv preprint arXiv:2305.03558_ , 2023.
  * [32] B. Series, “Method for the subjective assessment of intermediate quality level of audio systems,” _International Telecommunication Union Radiocommunication Assembly_ , 2014.
  * [33] B. Bernschütz, “A spherical far field HRIR/HRTF compilation of the neumann KU 100,” in _Proceedings of the 40th Italian (AIA) annual conference on acoustics and the 39th German annual conference on acoustics (DAGA) conference on acoustics_. German Acoustical Society (DEGA) Berlin, 2013, p. 29.
  * [34] M. R. Schroeder, “New method of measuring reverberation time,” _The Journal of the Acoustical Society of America_ , vol. 37, no. 6, pp. 1187–1188, 1965.
  * [35] B. Rafaely and A. Avni, “Interaural cross correlation in a sound field represented by spherical harmonics,” _The Journal of the Acoustical Society of America_ , vol. 127, no. 2, pp. 823–828, 2010.
  * [36] H. Keselman, J. Algina, and R. K. Kowalchuk, “The analysis of repeated measures designs: a review,” _British Journal of Mathematical and Statistical Psychology_ , vol. 54, no. 1, pp. 1–20, 2001.