Deep Learning-Based Approach for Identification and Compensation of Nonlinear Distortions in Parametric Array Loudspeakers

Jia-Xin Zhong; Jing Lu; Kai Chen; Mengtong Li; Tao Zhuang

REVIEW 3 major objections 3 minor 27 references

Deep Learning-Based Approach for Identification and Compensation of Nonlinear Distortions in Parametric Array Loudspeakers

T0 review · 3 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A feedforward WaveNet trained on measured audio identifies and inverts the nonlinearity of a parametric array loudspeaker, cutting average total harmonic distortion from 25.62% to 4.55%.

desk verdict Measured PAL distortion cut by a WaveNet inverse, but the Volterra baselines get 160x less training data, so part of the gap is training-effort inequality. read the letter →

arxiv 2412.01092 v1 pith:WCERERIF submitted 2024-12-02 eess.AS cs.SDcs.SYeess.SY

Mengtong Li , Tao Zhuang , Kai Chen , Jia-Xin Zhong , Jing Lu This is my paper · ORCID

classification eess.AScs.SDcs.SYeess.SY

keywords parametricarrayloudspeakernonlineardistortioncompensationWaveNetVolterrafiltertotalharmonicintermodulationdeeplearningsystemidentification

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

The paper claims that a feedforward WaveNet neural network can learn the full nonlinear input–output behavior of a parametric array loudspeaker (PAL) and can then be run as an inverse filter that pre-distorts the audio signal so the audible output is nearly linear. On measurements from 250 Hz to 8 kHz, the method lowers average total harmonic distortion from 25.62% to 4.55% and average intermodulation distortion from 12.05% to 2.47%, beating second- and third-order Volterra inverse filters at every tested frequency. The motivation is that a p-th order Volterra inverse removes low-order nonlinearities only by creating higher-order ones that still fold down into low-order harmonics, while a learned inverse is not restricted to a fixed polynomial order.

What carries the argument

The load-bearing object is a feedforward variant of WaveNet: a stack of dilated causal one-dimensional convolution layers, each followed by a gated tanh activation, pointwise convolutions, and residual connections, with receptive field $N=(M-1)\sum_{k=1}^{K}d_k+1$. The same architecture is used twice: a nine-block, 16-channel version identifies the PAL's nonlinear map, and a 24-block, 24-channel version acts as the inverse filter with a tanh output constraint that keeps the preprocessed signal inside the PAL's input range. Both are trained with a loss that combines mean squared error on the waveform with mean squared error on the spectrogram magnitudes; the inverse filter is trained against the linear target $y_{\mathrm{lin}}[n]$ from an LMS-fitted FIR model, and a 100-sample delay is inserted because the acoustic system is non-minimum phase and needs the delay for a stable causal inverse.

What would settle it

A reader could settle the claim by measuring the PAL's linear response independently (for instance with a low-level sweep that stays below the nonlinear threshold), comparing it with the LMS-FIR target $y_{\mathrm{lin}}$, and then repeating the whole compensation on a second PAL unit: if the FIR target deviates from the true linear response by an amount comparable to the residual distortion, or if the average THD and IMD do not again fall to roughly 4.55% and 2.47%, the reported reduction is at least partly an artifact of the chosen target.

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Extended reading notes

Core claim

The central discovery is that one WaveNet-based network can serve both roles in the compensation chain. The first network is trained on recorded input–output audio to predict the current output sample from a window of past input samples, and it reproduces the measured THD and IMD of the PAL within about 1.08 and 0.34 percentage points on average. The second network is then trained as the inverse filter: it maps the desired audio input to a preprocessed signal, and the loss compares the output of the first network on that preprocessed signal with a linear target $y_{\mathrm{lin}}[n]$ obtained from a separate FIR model of the PAL. When the resulting preprocessed audio is played through the physical PAL, the measured average THD falls to 4.55% and IMD to 2.47%, which the paper presents as the first demonstration that deep learning can bring PAL distortion below the level reached by Volterra inverses.

Load-bearing premise

The scheme rests on the assumption that the FIR linear model fitted by LMS gives the correct linear response of the PAL, because the inverse filter is trained to reproduce that model's output rather than any independently measured ideal.

Editorial extensions

If this is right

A learned inverse filter can replace Volterra-based preprocessing in PAL systems and reach distortions the polynomial filters do not.
Because the inverse is learned rather than truncated at a fixed order, harmonics of any order that fold back into the audible band are in principle handled by the same trained network.
The identified WaveNet model is accurate enough to stand in for the physical loudspeaker while designing the inverse, so compensation can be computed offline from recorded data.
The compensation leaves the linear frequency response essentially unchanged, so it can be inserted as a preprocessor without re-equalizing the loudspeaker.
In the speech- and music-relevant band below 4 kHz the average THD drops to about 5.47% and IMD to about 2.71%, where the improvement matters most for program material.

Reading between the lines

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

The paper does not test other modulation schemes; a natural extension is the same two-stage training for square-root or single-sideband AM, since the network learns from data rather than from Berktay's assumptions.
The paper does not separate network error from target-model bias; replacing the LMS-FIR linear target with a separately measured low-level linear response would directly check the residual 4.55% THD.
The inverse filter is demonstrated offline at one microphone position; real-time deployment would require checking stability as temperature, humidity, and transducer aging change the PAL's response.

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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 take: this is a solid, well-executed application of a known deep-learning architecture to a real acoustic-engineering problem. The authors train a feedforward WaveNet to model a parametric array loudspeaker, then use it to design an inverse filter. The identification surrogate is checked against physical measurements—average THD error 1.08%, IMD error 0.34%—and the compensated output is measured on the real loudspeaker, not just simulated. Average THD drops from 25.62% to 4.55% over 250 Hz–8 kHz, and IMD from 12.05% to 2.47%, beating the 2nd- and 3rd-order Volterra inverses. Those measured numbers are the paper's real asset.

What's new: prior neural work [20] used a 3-layer MLP and no distortion metrics; this paper brings a proper dilated causal convolutional architecture, reports quantitative THD/IMD, and validates on hardware. The two-stage identification-then-inversion loop is clean, and the amplitude constraint on the inverse output is a sensible practical addition.

Soft spots, in proportion. The most relevant is the comparison fairness. The Volterra kernels are identified from 45 s of white Gaussian noise, with no reported identification error or convergence check, while the WaveNet surrogate is trained on 2 h of matched audio (music, speech, ambient), and the inverse filter is trained on that same distribution. So the headline gap may partly reflect unequal training effort, not purely algorithmic superiority. That doesn't sink the paper—a full inverse should beat a truncated p-th-order inverse—but the quantitative magnitude is open to question, and the authors should be pressed on it. Also, the experiments are a single campaign with no error bars or repetitions, and no code or data are released. The linear target y_lin is obtained from an LMS-fitted FIR on the same data; if that fit is biased, the compensation target is biased, though the measured linear responses before/after look similar, which is reassuring.

The citation pattern is fine, and the paper is honest about the p-th-order inverse limitation. This is a credible, applied contribution for acoustics and audio DSP readers. It deserves a serious referee, with the baseline-training mismatch as the central point to resolve.

Referee Report

3 major / 3 minor

Summary. The paper proposes a two-stage deep-learning pipeline for parametric array loudspeakers (PALs): a feedforward WaveNet is first trained as a surrogate of the measured PAL input-output behavior, and a second WaveNet is then trained through this surrogate as an inverse filter whose output is amplitude-constrained and delayed by 100 samples. The compensation target is the output of an FIR linear model identified by LMS. Experiments in an anechoic chamber compare the proposed method with second- and third-order Volterra inverse filters, reporting average THD reduced from 25.62% to 4.55% and IMD from 12.05% to 2.47% over 250 Hz-8 kHz, with the deep method outperforming the Volterra baselines at all measured frequencies.

Significance. If the quantitative claims hold, this is a useful step for PAL nonlinear compensation because it replaces the pth-order inverse limitation of Volterra filters with a learned inverse, and it validates the result on physical measurements of a real loudspeaker rather than only on simulated outputs. The paper deserves credit for measuring the compensated output directly on the PAL, which provides an external benchmark and avoids purely circular evaluation, and for reporting a reasonably small identification error of the WaveNet surrogate (average 1.08% THD error and 0.34% IMD error in Fig. 6). However, the central comparative claim is weakened by the lack of validation of the Volterra baselines and by the absence of uncertainty quantification in Table I, so the significance is somewhat conditional.

major comments (3)

[§III-D and Table I] The Volterra baselines (VF2 and VF3) are identified from a single 45 s white-Gaussian-noise recording with NLMS (step size 0.01, kernel memories 160/80), but the paper reports no identification error, convergence check, or sensitivity analysis for these models, while the WaveNet surrogate is trained on 2 h of general audio. The headline comparison (4.55% vs 15.70%/12.04% THD; 2.47% vs 6.65%/4.87% IMD) is therefore not interpretable as an algorithmic advantage unless the VF baselines are shown to be reasonably optimized and the training conditions are made commensurable. Please report VF identification quality (e.g., measured versus predicted THD/IMD, kernel convergence over time, or repeated NLMS runs) and either match the training data or explicitly justify the mismatch.
[§II, Eq. (3) and Fig. 2(b)] The compensation target y_lin[n] is obtained from an FIR linear model identified by LMS on the same measured data, but the accuracy of this linear model is never quantified. If y_lin misestimates the true linear response of the PAL, the inverse filter will drive the loudspeaker toward a biased target, and the measured distortion reduction could reflect the choice of linear target rather than a genuine compensation of the physical system. Please report the fit error of the FIR linear model and, ideally, test the sensitivity of the measured THD/IMD to reasonable perturbations of y_lin.
[§III-B, Table I, Fig. 7] The central quantitative claim rests on single values in Table I with no repeated measurements, error bars, or confidence intervals. Since the measured THD and IMD are the primary evidence for the proposed method, the authors should report at least several repeated measurements for the before/after and baseline conditions, and state the resulting variability, so that the claimed 2.6x improvement in THD is statistically meaningful.

minor comments (3)

[§III-D] There are typographical errors, including 'specificed' for 'specified' and a duplicated 'and' in the sentence introducing y_lin and y_nlin in §II; these should be corrected.
[Fig. 6 and Fig. 7] The figures present curves without error bars or a statement of how many independent measurements were averaged; please clarify whether the plotted values are single trials, averages, and over what set of repetitions.
[§III-C] The sentence reporting 'average error in THD and IMD estimation are only 1.08% and 0.34%' should define the averaging domain (over frequencies and/or over trials) and state whether these are absolute or relative errors.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: final THD/IMD are physically measured, not defined by the fitted inverse.

full rationale

All load-bearing quantities are externally measured rather than defined by fitted parameters. Network 1 is trained on 2 h of measured input-output PAL data (Sections III-A and III-C) and validated against independent THD/IMD measurements (Fig. 6, with average errors of 1.08% and 0.34%). Network 2's inverse filter is trained through the learned surrogate to reproduce y_lin, an FIR/LMS linear target, but the paper's headline results—average THD 4.55% and IMD 2.47% after compensation—are measured on the physical PAL using step-sine and two-tone tests (Fig. 7 and Table I), so they cannot reduce to the training target by construction. The only internal coupling is that the inverse is optimized against the surrogate and a fitted linear target, which could bias the compensation if y_lin is inaccurate or surrogate error compounds; however, neither the target nor the surrogate is defined in terms of the measured THD/IMD used as the evaluation. The time-delay argument cites an independent room-impulse-response invertibility result [22]. No load-bearing uniqueness claim or self-citation chain appears; self-references [1, 4] are contextual. Unequal training-data volume between WaveNet and Volterra baselines is a possible experimental-design confound affecting the comparative claim, but it is not a circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The method has no invented physical entities. It relies on standard supervised training plus domain assumptions about the PAL (finite memory, non-minimum phase, and correctness of an FIR-derived linear target). Trained network weights are data-fitted by design and are not listed as free parameters; the listed items are hand-chosen design parameters that affect the reported performance.

free parameters (3)

Inverse filter time delay = 100 samples (2.3 ms)
Chosen by hand to keep the inverse stable and causal for a non-minimum phase system; it affects the timing and quality of compensation (Section III-D).
WaveNet architecture hyperparameters = 9/24 residual blocks; channels C=16/24; kernel M=16/4; dilations {1,2,...,256} and {1,...,2048} repeated
Selected by the authors without a reported hyperparameter search or ablation; they control model capacity and receptive field and therefore the distortion reduction.
Inverse output amplitude constraint scale = not reported
A Tanh activation after the linear mixer limits the preprocessed signal to the PAL input range, but the exact scaling is not given, so the effective constraint is a hand-set design element.

assumptions (4)

domain assumption The PAL behaves as a time-invariant causal nonlinear system with finite memory equal to the WaveNet receptive field.
The identification map in Eq. (1) and inverse map in Eq. (2) only use the current and past N input samples; no time-varying or infinite-memory behavior is modeled.
domain assumption The FIR plus LMS linear model produces the correct desired linear output y_lin[n].
Section II defines the inverse filter training loss against y_lin[n]; a biased linear target would be inherited by the compensation.
domain assumption The PAL and acoustic transmission form a non-minimum phase system, so a stable causal inverse requires a delay.
Section II cites [22] to justify the 100-sample delay used in both the WaveNet and Volterra inverse filters.
domain assumption A dilated causal convolutional network can approximate the PAL nonlinearity well enough for inverse training.
No approximation guarantees are stated; the architecture is transferred from tube amplifier modeling [17] and validated only by the identification errors in Fig. 6.

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Cite this review

Pith. "Pith review of Deep Learning-Based Approach for Identification and Compensation of Nonlinear Distortions in Parametric Array Loudspeakers." pith.science (2026). https://pith.science/paper/WCERERIF

@misc{pith2026241201092,
  author       = {Pith},
  title        = {Pith review of: Deep Learning-Based Approach for Identification and Compensation of Nonlinear Distortions in Parametric Array Loudspeakers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WCERERIF}},
  note         = {Machine review of arXiv:2412.01092}
}

read the original abstract

Compared to traditional electrodynamic loudspeakers, the parametric array loudspeaker (PAL) offers exceptional directivity for audio applications but suffers from significant nonlinear distortions due to its inherent intricate demodulation process. The Volterra filter-based approaches have been widely used to reduce these distortions, but the effectiveness is limited by its inverse filter's capability. Specifically, its pth-order inverse filter can only compensate for nonlinearities up to the pth order, while the higher-order nonlinearities it introduces continue to generate lower-order harmonics. In contrast, this paper introduces the modern deep learning methods for the first time to address nonlinear identification and compensation for PAL systems. Specifically, a feedforward variant of the WaveNet neural network, recognized for its success in audio nonlinear system modeling, is utilized to identify and compensate for distortions in a double sideband amplitude modulation-based PAL system. Experimental measurements from 250 Hz to 8 kHz demonstrate that our proposed approach significantly reduces both total harmonic distortion and intermodulation distortion of audio sound generated by PALs, achieving average reductions to 4.55% and 2.47%, respectively. This performance is notably superior to results obtained using the current state-of-the-art Volterra filter-based methods. Our work opens new possibilities for improving the sound reproduction performance of PALs.

Figures

Figures reproduced from arXiv: 2412.01092 by the authors.

**Figure 2.** Deep learning-based nonlinear system identification and compensation [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** The structure of the feedforward WaveNet. [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: A photo of the experimental setup. 1.8 m PULSE Multiplier input1 output input2 input2 input1 Power Amplifier output input Audio Carrier output1 output2 Ultrasound emitters Microphone [PITH_FULL_IMAGE:figures/full_fig_p003_4.png]

**Figure 5.** Figure 5: The signal flow of the measurement. pointwise (kernel size = 1) 1D convolution layer (P-Conv1d), the channel number of the input signal u[n] is adjusted from 1 to C. The adjusted signal then passes through a series of residual blocks, each comprising a 1D dilated convo…

**Figure 6.** Figure 6: The results of PAL system identification using WaveNet. (a) Measured [PITH_FULL_IMAGE:figures/full_fig_p004_6.png]

**Figure 7.** Figure 7: Results measured before and after compensation by inverse filters. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_7.png]

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

27 extracted references · 24 canonical work pages

[20]

Design of parametric acoustic array based on inverse control processing,

Z. Zhou and S. Chen, “Design of parametric acoustic array based on inverse control processing,” Appl. Acoust., vol. 195, p. 108816, 2022

work page 2022
[1]

Zhong and X

J. Zhong and X. Qiu, Acoustic Waves Generated by Parametric Array Loudspeakers. CRC Press, 2024

work page 2024
[2]

A review of parametric acoustic array in air,

W.-S. Gan, J. Yang, and T. Kamakura, “A review of parametric acoustic array in air,” Appl. Acoust., vol. 73, no. 12, pp. 1211–1219, 2012

2012
[3]

An overview of directivity control methods of the parametric array loudspeaker,

C. Shi, Y . Kajikawa, and W.-S. Gan, “An overview of directivity control methods of the parametric array loudspeaker,” APSIPA Trans. Signal Inf. Process., vol. 3, p. e20, 2014

work page 2014
[4]

Quiet zone generation in an acoustic free field using multiple parametric array loudspeakers,

J. Zhong, T. Zhuang, R. Kirby, M. Karimi, H. Zou, and X. Qiu, “Quiet zone generation in an acoustic free field using multiple parametric array loudspeakers,” J. Acoust. Soc. Am., vol. 151, no. 2, pp. 1235–1245, 2022

work page 2022
[5]

Carrier frequency influ- ence on the audible and ultrasonic fields generated by an omnidirectional parametric loudspeaker excited with exponential sine sweeps,

M. Arnela, C. Mart ´ınez-Suqu´ıa, and O. Guasch, “Carrier frequency influ- ence on the audible and ultrasonic fields generated by an omnidirectional parametric loudspeaker excited with exponential sine sweeps,” Appl. Acoust., vol. 200, p. 109073, 2022

work page 2022
[6]

Development of parametric loud- speaker for practical use,

T. Kamakura and M. Yoneyama, “Development of parametric loud- speaker for practical use,” in Proc. 10th Int. Symp. Nonlinear Acoust. , 1984, pp. 147–150

work page 1984
[7]

A study for the realization of a parametric loudspeaker,

T. Kamakura, Y . Tasahide, and K. Ikeyaya, “A study for the realization of a parametric loudspeaker,” J. Acoust. Soc. Jpn. , vol. 6, pp. 1–18, 1985

work page 1985

Show all 27 references

[8]

On preprocessing techniques for bandlim- ited parametric loudspeakers,

E.-L. Tan, P. Ji, and J. Yang, “On preprocessing techniques for bandlim- ited parametric loudspeakers,” Appl. Acoust., vol. 71, no. 5, pp. 486–492, 2010

2010
[9]

Possible exploitation of non-linear acoustics in underwa- ter transmitting applications,

H. O. Berktay, “Possible exploitation of non-linear acoustics in underwa- ter transmitting applications,” J. Sound Vib., vol. 2, no. 4, pp. 435–461, 1965

1965
[10]

Modeling nonlinearity of air with volterra kernels for use in a parametric array loudspeaker,

K. C.-M. Lee, J. Yang, W. S. Gan, and M.-H. Er, “Modeling nonlinearity of air with volterra kernels for use in a parametric array loudspeaker,” in Audio Engineering Society Convention 112. Audio Engineering Society, 2002

2002
[11]

Inverse system design based on the V olterra mod- eling of a parametric loudspeaker system,

W. Ji and W.-S. Gan, “Inverse system design based on the V olterra mod- eling of a parametric loudspeaker system,” AIP Conference Proceedings, vol. 1474, no. 1, pp. 383–386, 2012

2012
[12]

Modeling and compensation for the distortion of parametric loudspeakers using a one-dimension volterra filter,

Y . Mu, P. Ji, W. Ji, M. Wu, and J. Yang, “Modeling and compensation for the distortion of parametric loudspeakers using a one-dimension volterra filter,” IEEE/ACM Trans. Audio, Speech, Lang. Process., vol. 22, no. 12, pp. 2169–2181, 2014

2014
[13]

Identification of the parametric array loud- speaker with a volterra filter using the sparse nlms algorithm,

C. Shi and Y . Kajikawa, “Identification of the parametric array loud- speaker with a volterra filter using the sparse nlms algorithm,” in 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2015, pp. 3372–3376

2015
[14]

V olterra model of the parametric array loudspeaker operating at ultrasonic frequencies,

C. Shi and Y . Kajikawa, “V olterra model of the parametric array loudspeaker operating at ultrasonic frequencies,” J. Acoust. Soc. Am. , vol. 140, no. 5, pp. 3643–3650, 2016

2016
[15]

Compensation for nonlinear distor- tion of the frequency modulation-based parametric array loudspeaker,

Y . Hatano, C. Shi, and Y . Kajikawa, “Compensation for nonlinear distor- tion of the frequency modulation-based parametric array loudspeaker,” IEEE/ACM Trans. Audio, Speech, Lang. Process. , vol. 25, no. 8, pp. 1709–1717, 2017

2017
[16]

Universal approximation bounds for superpositions of a sigmoidal function,

A. Barron, “Universal approximation bounds for superpositions of a sigmoidal function,” IEEE Trans. Inf. Theory. , vol. 39, no. 3, pp. 930– 945, 1993

1993
[17]

Deep learning for tube amplifier emulation,

E.-P. Damsk ¨agg, L. Juvela, E. Thuillier, and V . V¨alim¨aki, “Deep learning for tube amplifier emulation,” inICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019, pp. 471–475

2019
[18]

Lightweight and in- terpretable neural modeling of an audio distortion effect using hy- perconditioned differentiable biquads,

S. Nercessian, A. Sarroff, and K. J. Werner, “Lightweight and in- terpretable neural modeling of an audio distortion effect using hy- perconditioned differentiable biquads,” in ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)...

2021
[19]

Pruning deep neural network models of guitar distortion effects,

D. S ¨udholt, A. Wright, C. Erkut, and V . V¨alim¨aki, “Pruning deep neural network models of guitar distortion effects,” IEEE/ACM Trans. Audio, Speech, Lang. Process., vol. 31, pp. 256–264, 2023

2023
[21]

Wavenet: A gener- ative model for raw audio,

A. v. d. Oord, S. Dieleman, H. Zen, K. Simonyan, O. Vinyals, A. Graves, N. Kalchbrenner, A. Senior, and K. Kavukcuoglu, “Wavenet: A gener- ative model for raw audio,” arXiv preprint arXiv:1609.03499 , 2016

2016 arXiv
[22]

Invertibility of a room impulse response,

S. T. Neely and J. B. Allen, “Invertibility of a room impulse response,” J. Acoust. Soc. Am. , vol. 66, no. 1, pp. 165–169, 1979

1979
[23]

The audio spotlight: An application of nonlinear interaction of sound waves to a new type of loudspeaker design,

M. Yoneyama, J.-i. Fujimoto, Y . Kawamo, and S. Sasabe, “The audio spotlight: An application of nonlinear interaction of sound waves to a new type of loudspeaker design,” J. Acoust. Soc. Am. , vol. 73, no. 5, pp. 1532–1536, 1983

1983
[24]

An experimental investigation about parameters’ effects on spurious sound in parametric loudspeaker,

P. Ji and J. Yang, “An experimental investigation about parameters’ effects on spurious sound in parametric loudspeaker,” Appl. Acoust. , vol. 148, pp. 67–74, 2019

2019
[25]

The nigens general sound events database,

I. Trowitzsch, J. Taghia, Y . Kashef, and K. Obermayer, “The nigens general sound events database,” arXiv preprint arXiv:1902.08314, 2019

1902 arXiv
[26]

Sound system equipment. part 5: Loudspeakers,

IEC 60268-5-2007, “Sound system equipment. part 5: Loudspeakers,” IEC, 2007

2007
[27]

Schetzen, The Volterra and Wiener Theories of Nonlinear Systems

M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems . Krieger Publishing Co., Inc., 2006

2006

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [20]

Design of parametric acoustic array based on inverse control processing,

Z. Zhou and S. Chen, “Design of parametric acoustic array based on inverse control processing,” Appl. Acoust., vol. 195, p. 108816, 2022

work page 2022

[2] [1]

Zhong and X

J. Zhong and X. Qiu, Acoustic Waves Generated by Parametric Array Loudspeakers. CRC Press, 2024

work page 2024

[3] [2]

A review of parametric acoustic array in air,

W.-S. Gan, J. Yang, and T. Kamakura, “A review of parametric acoustic array in air,” Appl. Acoust., vol. 73, no. 12, pp. 1211–1219, 2012

2012

[4] [3]

An overview of directivity control methods of the parametric array loudspeaker,

C. Shi, Y . Kajikawa, and W.-S. Gan, “An overview of directivity control methods of the parametric array loudspeaker,” APSIPA Trans. Signal Inf. Process., vol. 3, p. e20, 2014

work page 2014

[5] [4]

Quiet zone generation in an acoustic free field using multiple parametric array loudspeakers,

J. Zhong, T. Zhuang, R. Kirby, M. Karimi, H. Zou, and X. Qiu, “Quiet zone generation in an acoustic free field using multiple parametric array loudspeakers,” J. Acoust. Soc. Am., vol. 151, no. 2, pp. 1235–1245, 2022

work page 2022

[6] [5]

Carrier frequency influ- ence on the audible and ultrasonic fields generated by an omnidirectional parametric loudspeaker excited with exponential sine sweeps,

M. Arnela, C. Mart ´ınez-Suqu´ıa, and O. Guasch, “Carrier frequency influ- ence on the audible and ultrasonic fields generated by an omnidirectional parametric loudspeaker excited with exponential sine sweeps,” Appl. Acoust., vol. 200, p. 109073, 2022

work page 2022

[7] [6]

Development of parametric loud- speaker for practical use,

T. Kamakura and M. Yoneyama, “Development of parametric loud- speaker for practical use,” in Proc. 10th Int. Symp. Nonlinear Acoust. , 1984, pp. 147–150

work page 1984

[8] [7]

A study for the realization of a parametric loudspeaker,

T. Kamakura, Y . Tasahide, and K. Ikeyaya, “A study for the realization of a parametric loudspeaker,” J. Acoust. Soc. Jpn. , vol. 6, pp. 1–18, 1985

work page 1985