Binaural Signal Matching with Wearable Arrays for Near-Field Sources

Boaz Rafaely; David Lou Alon; Sapir Goldring; Zamir Ben Hur

REVIEW 3 major objections 4 minor 14 references

Binaural Signal Matching with Wearable Arrays for Near-Field Sources

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Accounting for source distance in binaural signal matching sharply cuts reproduction error for close talkers.

desk verdict A clean near-field extension of BSM whose headline gain is only shown against the same model used to design the filters; worth a careful revision, not a dismissal. read the letter →

arxiv 2507.15517 v1 pith:TOIDIOKU submitted 2025-07-21 eess.AS

Sapir Goldring , Zamir Ben Hur , David Lou Alon , Boaz Rafaely This is my paper · ORCID

classification eess.AS

keywords binauralreproductionnear-fieldsignalmatchingwearablemicrophonearraysrigid-spheremodeldistancevariationfunctionhead-relatedtransferfunctionsvirtualreality

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper extends Binaural Signal Matching (BSM), an algorithm that renders binaural audio over headphones from arbitrary microphone arrays, to near-field sound sources whose wavefronts are spherical rather than planar. It shows in simulation that the standard far-field BSM keeps binaural error acceptably low for sources down to a few tens of centimeters, but error climbs sharply for closer sources. Replacing the far-field steering vectors and HRTFs with near-field versions that include the source distance substantially lowers the error at these close distances. The demonstration uses a four-microphone semi-circular array on a rigid sphere that models a head-mounted device; the authors note that even near-field BSM leaves high error when the source is only a few centimeters from the array.

What carries the argument

The mechanism is the BSM matched-filter solution of Eq. (6), together with the near-field acoustic model used to populate its two inputs. The steering matrix $V_{\mathrm{nf}}$ is computed directly from the rigid-sphere analytical pressure solution of Eq. (16) for a point source at distance $r_s$; the near-field HRTF is obtained by multiplying a measured far-field HRTF by the directional variation function DVF (Eq. 15), which is the ratio of rigid-sphere pressures at near and far distances (Eq. 17). These two model ingredients carry the argument because both the simulated ground-truth binaural signal and the near-field BSM filter are built from them.

What would settle it

Measure near-field HRTFs and microphone array transfer functions on a physical manikin or human subject at source distances 0.15, 0.2, 0.5, and 3.2 m using the same four-microphone semi-circular geometry. Use the measured transfer functions to generate both the ground-truth binaural signals and the far-field and near-field BSM filters, then compare normalized MSE below 2 kHz. If near-field BSM does not beat far-field BSM at close distances, the simulated advantage is an artifact of using the same rigid-sphere/DVF model for both truth and filters.

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Extended reading notes

Core claim

The paper's central claim is that BSM, originally formulated for plane-wave sources, can be adapted to near-field point sources by substituting the near-field steering matrix $V_{\mathrm{nf}}(k,\Omega,r_s)$ and near-field HRTFs $[h^{l/r}_{\mathrm{nf}}]$ into the optimal MSE filter $c^{l/r} = (VV^H + \sigma_n^2/\sigma_s^2 I_M)^{-1} V [h^{l/r}]^*$. The near-field quantities are generated analytically from the rigid-sphere pressure solution of Eq. (16) and from far-field HRTFs scaled by the distance variation function of Eq. (17). In simulation with a four-microphone semi-circular array on a 0.1 m rigid sphere, the near-field filter reduces normalized MSE below 2 kHz relative to the far-field filter at source distances from 0.15 m to 3.2 m, with the largest gains at 0.15 m and 0.2 m. The paper also reports that at extreme close range the near-field filter still has substantial remaining error, attributed to factors not captured by the model.

Load-bearing premise

The load-bearing premise is that the rigid-sphere pressure solution and the distance-scaling formula (DVF) accurately describe true near-field sound around a human head; because the same model generates both the simulated reference signals and the near-field filters, the reported error reduction could reflect model self-consistency rather than real-world accuracy.

Editorial extensions

If this is right

If the claimed error reduction holds, close-talk binaural rendering from head-worn microphone arrays can be improved without changing the array geometry, by supplying an estimate of the source distance.
Below roughly 2 kHz, near-field BSM consistently beats far-field BSM at all simulated near-field distances, with the largest improvement at 0.15-0.2 m.
At frequencies above 2 kHz, reproduction error remains large regardless of near-field modeling, because the HRTF spherical-harmonics order exceeds what a four-microphone array can capture.
For sources beyond tens of centimeters, far-field BSM is adequate, so near-field modeling matters mainly for very close sources.
At extreme near-field distances, where the source is within a few centimeters of the array surface, even near-field BSM leaves high binaural error, motivating further investigation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the simulated ground truth and the near-field BSM filter share the same rigid-sphere/DVF model, the reported advantage may overstate what a real listener would hear; a measurement-based evaluation with a manikin or human subject at 0.15-0.2 m would test this.
The DVF-based near-field HRTF model scales only the distance-dependent pressure of a measured far-field HRTF, while real near-field HRTFs also include head, torso, and pinna interactions that the rigid sphere omits, so the gap between far-field and near-field BSM may change in realistic conditions.
Since the near-field BSM filter depends explicitly on the source distance $r_s$, practical deployment would require a distance estimator or a bank of filters computed at candidate distances.
The same substitution of near-field steering vectors and HRTFs could be applied to arbitrary array geometries beyond the semi-circular rigid-sphere configuration, because the BSM formulation itself does not constrain array shape.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a modest, clearly written extension of Binaural Signal Matching to near-field sources, and the math is coherent. The issue that matters is external validity: the near-field filters and the simulated ground truth are built from the same rigid-sphere/DVF model, so the reported advantage of NF BSM over FF BSM is, at least partly, model self-consistency. Still, the paper is honest and the distance sweep is useful.

What's actually new: prior BSM work [1] assumes plane waves; this is the first to plug near-field point-source steering vectors and near-field HRTFs into the BSM filter formula. The derivation of Eqs. (12)-(14) is standard. Using DVF scaling for HRTFs and the analytic rigid-sphere pressure for steering is a reasonable simulation strategy, and the authors don't oversell—they note the error grows again at 5-10 cm and call for a listening test.

The soft spots, in order of importance. First, the circularity: the target binaural signals in Eq. (10) are synthesized with exactly the same h_nf used in the NF BSM filter of Eq. (14). So any mismatch between the DVF/rigid-sphere model and a real head, pinna, and wearable array is invisible. At the closest distances, where the paper claims the biggest benefit, the model is most likely to be wrong. That doesn't make the math wrong, but it does mean the headline improvement is unvalidated outside the model. Second, the paper omits the noise-to-signal ratio used in Eq. (6), shows only left-ear error, and gives no error bars; the simulation is deterministic, so error bars would need multiple noise realizations, but the omission is still a reproducibility gap. Third, the evaluation is entirely synthetic; measured near-field HRTFs or a different acoustic model would have strengthened the claim considerably.

On balance: this is a small but real step forward for a specific subfield, and the authors have been appropriately cautious about their conclusions. It deserves peer review, but I'd send it back for a revision that addresses the external-validity gap and fills in the missing experimental details. If the authors can show the effect persists with a mismatched model or measured data, the result becomes much more interesting. Who will get value: people working on binaural rendering for head-worn devices and near-field spatial audio. I'd cite it if I worked in that area; I wouldn't bring it to reading group as a methodological model.

Referee Report

3 major / 4 minor

Summary. The paper extends the Binaural Signal Matching (BSM) algorithm to near-field sources by replacing the far-field steering matrix and HRTFs in the filter design with near-field versions obtained from a rigid-sphere analytical model and a Distance Variation Function (DVF) scaling of far-field HRTFs. A simulation study with a four-microphone semicircular array mounted on a rigid sphere evaluates both far-field and near-field BSM filters for source distances from 0.15 m to 3.2 m, reporting normalized binaural MSE as a function of frequency. The central claim is that incorporating near-field information in BSM significantly reduces binaural error for close sources, while far-field BSM remains adequate for sources at moderate distances.

Significance. If the result holds, the paper provides a useful extension of BSM to near-field scenarios, which is practically relevant for wearable arrays and close-talk applications in VR and teleconferencing. The mathematical formulation is standard and the derivation of the near-field filter is a straightforward substitution into the existing BSM framework. The work also correctly identifies the limitation of far-field assumptions at short distances. However, the significance is limited by the fact that the entire evaluation is performed in simulation using the same rigid-sphere/DVF model that generates both the filters and the ground-truth signals, so the reported improvement may partly reflect model self-consistency rather than true reproduction accuracy in real acoustic scenes.

major comments (3)

[§IV and Eqs. (9), (10), (12), (14), (16), (17)] The evaluation is circular with respect to the near-field model. The ground-truth binaural signals in Eq. (10) are synthesized using the near-field HRTF h_nf from Eq. (17), and the microphone signals in Eq. (9) are generated using the near-field steering matrix V_nf from Eq. (16). The NF BSM filters in Eq. (14) are designed with the very same V_nf and h_nf. Any error in the rigid-sphere/DVF approximation is therefore invisible: the filter is tested against the exact model it was derived from. The reported advantage of NF BSM over FF BSM may be an artifact of this self-consistency. The paper should validate the claim with measured near-field HRTFs or, at minimum, perform a robustness study that introduces model mismatch (e.g., different head radius, microphone placement errors, or DVF inaccuracies) to show the benefit persists outside the generating model. As written, the central claim about real-world improvement is not supported by the evidence.
[§IV.A and Eq. (6)] The noise-to-signal power ratio σ_n^2/σ_s^2 is a free parameter in the BSM filter (Eq. (6)) and directly affects the MSE in Eq. (8), yet the simulation setup never specifies its value or whether noise is actually added to the microphone signals. Without this value, the results are not reproducible, and it is impossible to assess whether the comparison between FF BSM and NF BSM is performed under a fair or favorable regularization. The paper should state the ratio used, or report results across a range of ratios to show the qualitative conclusions are robust.
[§IV.B and Fig. 1] The paper reports only the left-ear MSE and does not specify the source directions used in the simulation. Since the array is not symmetric between left and right (microphone azimuths 30°, 80°, 280°, 330°), the right-ear error may differ, and the conclusion that binaural reproduction improves may depend on which ear is evaluated. Please report both ears or explain why left-ear results are representative, and specify the source azimuth/elevation in the simulation setup.

minor comments (4)

[Abstract and §I] The abstract contains a grammatical error: 'Analysis ... show' should be 'Analysis ... shows'. Also, in the introduction, the phrase 'Transfer Functiong' should be 'Transfer Functions'.
[§III.B, Eq. (15)] The notation for distances is inconsistent: Eq. (15) uses r_n and r_f, while the text later uses r_s and r_a. Please define all radial variables in one place and use them consistently throughout.
[§IV.A] The simulation appears to use a narrowband frequency-domain model, but the text mentions the need for broadband sources when discussing experimental challenges. Please clarify whether the error in Eq. (8) is computed per frequency bin and whether any time-domain or broadband processing is involved.
[Fig. 1] The figure caption describes solid and dashed lines, but the figure itself (as reproduced) has no legend or labels identifying which distance corresponds to which curve. Adding a legend or distance labels would improve readability.

Circularity Check

1 steps flagged · score 6.0 of 10

The reported NF-BSM advantage rests on an evaluation in which the same rigid-sphere/DVF model generates both the filters and the ground-truth binaural signals.

self definitional [Section III, Eqs. (9), (10), (14), (16), (17); Section IV simulation]
"The true binaural signal, specified in (2), becomes: pl/r(k) = [hl/r nf (k)]T s(k), (10) ... The filter coefficients are again computed using Eq. (6), but with the substitutions: V = Vnf, [hl/r] = [hl/r]nf ... cl/r nf = (VnfVH nf + σ2 n σ2s IM)^-1 Vnf[hl/r]∗ nf. (14) ... Near-field HRTFs are modeled by scaling far-field HRTFs with the DVF: hl/r(rn, θ, ϕ, k) = DVF(rn, rf , θ, ϕ, k, ra) · hl/r(rf , θ, ϕ, k). (17)"

The same near-field model is used on both sides of the evaluation. The near-field HRTF target in Eq. (10) is generated by DVF scaling (Eq. 17), and the NF BSM filter in Eq. (14) is designed from that same DVF-scaled HRTF together with the rigid-sphere steering matrix of Eq. (16). The microphone signals in Eq. (9) are also synthesized from the same rigid-sphere steering model. Therefore, the NF BSM filter is the MMSE solution for exactly the model used to create the 'true' binaural signals and the array observations. The reported error reduction over FF BSM is thus an in-sample, model-consistency comparison: any mismatch between the DVF/rigid-sphere approximation and real measured near-field HRTFs is invisible to the simulation.

full rationale

The derivation of the NF BSM filter is mathematically coherent, and no parameter is fitted to measured data. The circularity is in the evaluation: the ground-truth binaural signals (Eq. 10) and the NF BSM filter (Eq. 14) both use the near-field HRTF from Eq. (17), and both the filter design and the simulated microphone signals (Eq. 9) use the rigid-sphere steering model of Eq. (16). Hence the NF filter is tested against the very model from which it is constructed, which can inflate the apparent advantage over far-field BSM. The paper itself acknowledges that obtaining experimental near-field HRTFs is challenging and calls for future listening tests, which supports interpreting the current simulation as a model self-consistency check rather than real-world validation. Score 6 reflects a central evaluation that reduces to same-model agreement, not a score of 8-10 because the internal mathematics is consistent and the DVF/rigid-sphere building blocks come from prior independent work.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central result rests on the rigid-sphere acoustic model, the DVF near-field HRTF model, and the standard BSM statistical assumptions. The most consequential modeling overhead is using the same model for both simulated data and NF filters, which is listed as a circularity red flag.

free parameters (6)

Rigid sphere radius r_a = 0.1 m
Chosen head-radius model; source distances are measured from the origin, so a 0.15 m source is only 5 cm from the head surface.
Microphone azimuth positions = [30, 80, 280, 330] degrees, M = 4
Ad hoc semi-circular geometry approximating head-worn arrays; no sensitivity analysis over geometry is provided.
Spherical harmonic truncation order N = 30
Truncation chosen for the simulation; the paper notes error above 2 kHz is large, which depends on this order.
Noise-to-signal power ratio sigma_n^2 / sigma_s^2 = not stated
Appears in the BSM filter Eq. (6) and error expression Eq. (8), but the simulation never reports the value used.
Reference far-field distance r_f = 3.2 m
Used in the DVF to scale far-field HRTFs; assumed equal to the measurement distance of the KU100 database.
Source distances tested = 0.15 to 3.2 m
Chosen to span near-field to far-field; the 3.2 m case acts as the far-field reference.

assumptions (5)

domain assumption Far-field HRTFs from the Neumann KU100 database are valid for a generic listener.
Used as the baseline in Eq. (17); individual HRTFs vary, so results may differ across listeners.
domain assumption The rigid sphere is an adequate acoustic model for the head.
Underpins both the pressure solution in Eq. (16) and the DVF near-field HRTFs; torso and pinna effects are neglected.
domain assumption The DVF can synthesize near-field HRTFs by scaling far-field HRTFs.
Borrowed from Kan et al. [12]; introduces model dependence not independently validated here.
standard math The analytical point-source pressure on a rigid sphere, Eq. (16), is correct.
Standard wave-scattering result from [10]; not re-derived in this paper.
domain assumption Sources are uncorrelated with each other and with spatially white noise.
Required for the closed-form BSM filter Eq. (6), inherited from [1].

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Cite this review

Pith. "Pith review of Binaural Signal Matching with Wearable Arrays for Near-Field Sources." pith.science (2026). https://pith.science/paper/TOIDIOKU

@misc{pith2026250715517,
  author       = {Pith},
  title        = {Pith review of: Binaural Signal Matching with Wearable Arrays for Near-Field Sources},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TOIDIOKU}},
  note         = {Machine review of arXiv:2507.15517}
}

read the original abstract

Binaural reproduction methods aim to recreate an acoustic scene for a listener over headphones, offering immersive experiences in applications such as Virtual Reality (VR) and teleconferencing. Among the existing approaches, the Binaural Signal Matching (BSM) algorithm has demonstrated high quality reproduction due to its signal-independent formulation and the flexibility of unconstrained array geometry. However, this method assumes far-field sources and has not yet been investigated for near-field scenarios. This study evaluates the performance of BSM for near-field sources. Analysis of a semi-circular array around a rigid sphere, modeling head-mounted devices, show that far-field BSM performs adequately for sources up to approximately tens of centimeters from the array. However, for sources closer than this range, the binaural error increases significantly. Incorporating a near-field BSM design, which accounts for the source distance, significantly reduces the error, particularly for these very-close distances, highlighting the benefits of near-field modeling in improving reproduction accuracy.

Figures

Figures reproduced from arXiv: 2507.15517 by the authors.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages

[1]

Design and Analysis of Binaural Signal Matching with Arbitrary Microphone Arrays and Listener Head Rotations

L. Madmoni, Z. Ben-Hur, J. Donley, V . Tourbabin, and B. Rafaely, “De- sign and analysis of binaural signal matching with arbitrary microphone arrays,” arXiv preprint arXiv:2408.03581 , 2024

work page Pith review arXiv 2024
[2]

Spatial audio signal processing for binaural reproduction of recorded acoustic scenes– review and challenges,

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

work page 2022
[3]

Audio signal processing in the 21st century: The important outcomes of the past 25 years,

G. Richard, P. Smaragdis, S. Gannot, P. A. Naylor, S. Makino, W. Keller- mann, and A. Sugiyama, “Audio signal processing in the 21st century: The important outcomes of the past 25 years,” IEEE Signal Processing Magazine, vol. 40, no. 5, pp. 12–26, 2023

work page 2023
[4]

Spectral equalization in binaural signals represented by order-truncated spherical harmonics,

Z. Ben-Hur, F. Brinkmann, J. Sheaffer, S. Weinzierl, and B. Rafaely, “Spectral equalization in binaural signals represented by order-truncated spherical harmonics,” The Journal of the Acoustical Society of America , vol. 141, no. 6, pp. 4087–4096, 2017

work page 2017
[5]

Three-dimensional surround sound systems based on spherical harmonics,

M. A. Poletti, “Three-dimensional surround sound systems based on spherical harmonics,” Journal of the audio engineering society , vol. 53, no. 11, pp. 1004–1025, 2005

work page 2005
[6]

Interaural cross correlation in a sound field represented by spherical harmonics,

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

work page 2010
[7]

Using beamforming and binaural synthesis for the psychoacoustical evaluation of target sources in noise,

W. Song, W. Ellermeier, and J. Hald, “Using beamforming and binaural synthesis for the psychoacoustical evaluation of target sources in noise,” The Journal of the Acoustical Society of America , vol. 123, no. 2, pp. 910–924, 2008

work page 2008
[8]

On the selection of the number of beamform- ers in beamforming-based binaural reproduction,

I. Ifergan and B. Rafaely, “On the selection of the number of beamform- ers in beamforming-based binaural reproduction,” EURASIP Journal on Audio, Speech, and Music Processing , vol. 2022, no. 1, p. 6, 2022

work page 2022

Show all 14 references

[9]

Para- metric ambisonic encoding of arbitrary microphone arrays,

L. McCormack, A. Politis, R. Gonzalez, T. Lokki, and V . Pulkki, “Para- metric ambisonic encoding of arbitrary microphone arrays,” IEEE/ACM Transactions on Audio, Speech, and Language Processing , vol. 30, pp. 2062–2075, 2022

2022
[10]

Near-field spherical microphone array pro- cessing with radial filtering,

E. Fisher and B. Rafaely, “Near-field spherical microphone array pro- cessing with radial filtering,” IEEE Transactions on Audio, Speech, and Language Processing, vol. 19, no. 2, pp. 256–265, 2010

2010
[11]

Rafaely, Fundamentals of spherical array processing

B. Rafaely, Fundamentals of spherical array processing . Springer, 2015, vol. 8

2015
[12]

A psychophysical evaluation of near-field head-related transfer functions synthesized using a distance variation function,

A. Kan, C. Jin, and A. van Schaik, “A psychophysical evaluation of near-field head-related transfer functions synthesized using a distance variation function,” The Journal of the Acoustical Society of America , vol. 125, no. 4, pp. 2233–2242, 2009

2009
[13]

Near-field virtual audio displays,

D. S. Brungart, “Near-field virtual audio displays,” Presence, vol. 11, no. 1, pp. 93–106, 2002

2002
[14]

A spherical far field hrir/hrtf compilation of the neumann ku 100,

B. Bernsch ¨utz, “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 , vol. 29. German Acoustical Society ...

2013

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Design and Analysis of Binaural Signal Matching with Arbitrary Microphone Arrays and Listener Head Rotations

L. Madmoni, Z. Ben-Hur, J. Donley, V . Tourbabin, and B. Rafaely, “De- sign and analysis of binaural signal matching with arbitrary microphone arrays,” arXiv preprint arXiv:2408.03581 , 2024

work page Pith review arXiv 2024

[2] [2]

Spatial audio signal processing for binaural reproduction of recorded acoustic scenes– review and challenges,

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

work page 2022

[3] [3]

Audio signal processing in the 21st century: The important outcomes of the past 25 years,

G. Richard, P. Smaragdis, S. Gannot, P. A. Naylor, S. Makino, W. Keller- mann, and A. Sugiyama, “Audio signal processing in the 21st century: The important outcomes of the past 25 years,” IEEE Signal Processing Magazine, vol. 40, no. 5, pp. 12–26, 2023

work page 2023

[4] [4]

Spectral equalization in binaural signals represented by order-truncated spherical harmonics,

Z. Ben-Hur, F. Brinkmann, J. Sheaffer, S. Weinzierl, and B. Rafaely, “Spectral equalization in binaural signals represented by order-truncated spherical harmonics,” The Journal of the Acoustical Society of America , vol. 141, no. 6, pp. 4087–4096, 2017

work page 2017

[5] [5]

Three-dimensional surround sound systems based on spherical harmonics,

M. A. Poletti, “Three-dimensional surround sound systems based on spherical harmonics,” Journal of the audio engineering society , vol. 53, no. 11, pp. 1004–1025, 2005

work page 2005

[6] [6]

Interaural cross correlation in a sound field represented by spherical harmonics,

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

work page 2010

[7] [7]

Using beamforming and binaural synthesis for the psychoacoustical evaluation of target sources in noise,

W. Song, W. Ellermeier, and J. Hald, “Using beamforming and binaural synthesis for the psychoacoustical evaluation of target sources in noise,” The Journal of the Acoustical Society of America , vol. 123, no. 2, pp. 910–924, 2008

work page 2008

[8] [8]

On the selection of the number of beamform- ers in beamforming-based binaural reproduction,

I. Ifergan and B. Rafaely, “On the selection of the number of beamform- ers in beamforming-based binaural reproduction,” EURASIP Journal on Audio, Speech, and Music Processing , vol. 2022, no. 1, p. 6, 2022

work page 2022