Speech-preserving active noise control: a deep learning approach in reverberant environments
Pith reviewed 2026-05-10 15:55 UTC · model grok-4.3
The pith
A convolutional recurrent network for active noise control reduces noise while preserving target speech in reverberant rooms.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The Deep ANC system, built around a Convolutional Recurrent Network with LSTM for time-related acoustic features and complex spectrum mapping to address nonlinear paths, combined with a voice retention loss function, achieves significantly better noise reduction than the FxLMS algorithm, particularly for non-stationary noises like crowd babble, while PESQ and STOI evaluations confirm that both the naturalness and intelligibility of the target speech are preserved in reverberant environments created via the Image Source Method.
What carries the argument
Convolutional Recurrent Network (CRN) with LSTM layers and complex spectrum mapping, trained end-to-end using a voice retention loss function that identifies spectral speech features to suppress noise selectively.
If this is right
- The system handles broadband and non-stationary noises more effectively than linear adaptive filters.
- Target speech remains natural and intelligible according to PESQ and STOI evaluations.
- End-to-end training integrates noise cancellation and speech retention without separate processing stages.
- The approach applies to complex nonlinear acoustic paths that include reverberation effects.
Where Pith is reading between the lines
- If the simulation-to-reality gap proves small, the method could support real-time noise cancellation in shared spaces without interrupting conversations.
- The voice retention loss design offers a reusable pattern for other audio tasks that must balance aggressive noise removal against signal fidelity.
- Physical hardware tests with actual room impulse responses would be needed to confirm whether the reported gains hold outside simulated conditions.
- Combining the CRN with multi-microphone arrays could extend the approach to larger or more variable environments.
Load-bearing premise
The Image Source Method simulation with added reverberation accurately represents real-world acoustic environments and the custom voice retention loss function reliably identifies and preserves speech characteristics without overfitting to the simulated data.
What would settle it
Deploy the trained model on physical microphones and speakers in a real reverberant room, mix target speech with crowd babble noise, measure noise reduction and speech metrics against FxLMS, and check whether performance gaps seen in simulation persist or shrink.
read the original abstract
Traditional Active Noise Control (ANC) systems are mostly based on FxLMS algorithms, but such algorithms rely on linear assumptions and are often limited in handling broadband non-stationary noise or nonlinear acoustic paths. Not only that, the traditional method is used to eliminating all signals together, and noise reduction often accidentally damages the voice signal and affects normal communication. To tackle these issues, this study proposes a speech preserving deep learning ANC system, which aims to achieve stable noise reduction while effectively retaining speech in a complex acoustic environment. This study builds an end-to-end control architecture, the core of which adopts a Convolutional Recurrent Network (CRN). The structure uses the long short-term memory (LSTM) network to capture the time-related characteristics of acoustic signals. Combined with complex spectrum mapping (CSM) technology, the nonlinear distortion problem is effectively solved. In order to retain useful voice while removing noise, this study also designs a special voice retention loss function. This design guidance model selectively retains the target voice while suppressing environmental noise by identifying the characteristics of the spectrum structure. In addition, in order to verify whether the system is effective in real scenes, we use the Image Source Method (ISM) to build a high-fidelity acoustic simulation environment, which also simulates the real reverberation effect. Experimental results demonstrate that the proposed Deep ANC system achieves significantly better noise reduction than the traditional FxLMS algorithm, especially for non-stationary noises like crowd babble. Meanwhile, PESQ and STOI based evaluations confirm that the system preserves both the naturalness and intelligibility of the target speech.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript proposes a speech-preserving active noise control (ANC) system based on a Convolutional Recurrent Network (CRN) that incorporates complex spectrum mapping to handle nonlinear acoustic paths and a custom voice retention loss function to selectively preserve speech while suppressing noise. The approach is evaluated in simulated reverberant environments generated using the Image Source Method (ISM), with claims of superior noise reduction compared to the FxLMS algorithm, particularly for non-stationary noises, and maintained speech intelligibility and naturalness as measured by PESQ and STOI.
Significance. Should the performance gains be confirmed with real acoustic data and detailed quantitative analysis, this work could contribute to the development of more effective ANC systems for environments requiring simultaneous noise cancellation and speech communication. The use of deep learning to address limitations of linear adaptive filters like FxLMS is a relevant direction in the field. The end-to-end CRN architecture with CSM is a positive technical choice for modeling temporal and nonlinear effects.
major comments (3)
- [Abstract] Abstract: The central claims of 'significantly better noise reduction' than FxLMS and speech preservation confirmed by 'PESQ and STOI based evaluations' are presented without any numerical values, effect sizes, training details, statistical tests, or baseline comparisons, which is load-bearing for the superiority assertion.
- [Simulation and Experimental Validation] Simulation environment description: The assertion that ISM generates 'high-fidelity' reverberation simulating 'real scenes' is central to the validation of effectiveness in reverberant environments, yet ISM omits surface scattering, frequency-dependent absorption, microphone/loudspeaker nonlinearities, and time-varying responses, with no measured RIR cross-validation or physical-room experiments described.
- [Proposed Method] Voice retention loss function: The custom loss is introduced to identify and preserve speech spectral characteristics, but no ablation on the balancing coefficients, sensitivity analysis, or checks against overfitting to the synthetic ISM spectra are provided, undermining assessment of whether reported PESQ/STOI gains are robust.
minor comments (2)
- [Proposed Method] The CRN architecture description would benefit from explicit input/output tensor dimensions and the precise mathematical definition of the complex spectrum mapping operation.
- [Introduction] Additional references to prior deep-learning ANC works would better situate the novelty of the voice retention loss relative to existing spectrum-mapping approaches.
Simulated Author's Rebuttal
We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment point by point below, indicating the revisions we plan to incorporate to improve the clarity, rigor, and transparency of the work.
read point-by-point responses
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Referee: [Abstract] Abstract: The central claims of 'significantly better noise reduction' than FxLMS and speech preservation confirmed by 'PESQ and STOI based evaluations' are presented without any numerical values, effect sizes, training details, or baseline comparisons, which is load-bearing for the superiority assertion.
Authors: We agree that the abstract would be strengthened by including quantitative support for the claims. In the revised manuscript, we will update the abstract to report specific metrics from our experiments, including average noise reduction in dB (with effect sizes relative to FxLMS for stationary and non-stationary noises such as babble), PESQ and STOI scores for the proposed system versus the baseline, and a concise note on the training configuration (e.g., dataset size, epochs, and optimizer). These values are available from our results and will be added without altering the overall length significantly. revision: yes
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Referee: [Simulation and Experimental Validation] Simulation environment description: The assertion that ISM generates 'high-fidelity' reverberation simulating 'real scenes' is central to the validation of effectiveness in reverberant environments, yet ISM omits surface scattering, frequency-dependent absorption, microphone/loudspeaker nonlinearities, and time-varying responses, with no measured RIR cross-validation or physical-room experiments described.
Authors: We acknowledge the limitations of the Image Source Method (ISM) as a simulation tool. ISM is a standard approximation in acoustic modeling but does not capture surface scattering, frequency-dependent absorption, or hardware nonlinearities. We will revise the manuscript language to describe the setup as 'simulated reverberant environments generated via the Image Source Method' and remove overstated terms such as 'high-fidelity' and 'real scenes.' A new paragraph will be added to the discussion section explicitly noting these simplifications and stating that real-room validation with measured RIRs remains important future work. No physical experiments or cross-validation with measured data were performed, as the study focuses on the deep learning approach under controlled simulated conditions. revision: partial
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Referee: [Proposed Method] Voice retention loss function: The custom loss is introduced to identify and preserve speech spectral characteristics, but no ablation on the balancing coefficients, sensitivity analysis, or checks against overfitting to the synthetic ISM spectra are provided, undermining assessment of whether reported PESQ/STOI gains are robust.
Authors: We agree that additional analysis of the voice retention loss would improve assessment of its robustness. In the revised manuscript, we will add an ablation study section that varies the balancing coefficients (e.g., weights between speech preservation and noise suppression terms) and reports resulting changes in PESQ and STOI. We will also include sensitivity analysis plots and a discussion addressing potential overfitting to ISM-generated spectra, explaining the loss design based on general spectral structure priors and any regularization applied during training. These additions will be supported by new experimental results. revision: yes
Circularity Check
No significant circularity; empirical DL model evaluated against external baseline
full rationale
The paper describes an end-to-end CRN-based deep learning architecture for ANC, augmented by complex spectrum mapping and a custom voice-retention loss. Training and testing occur on data synthesized via the Image Source Method, with performance measured by direct comparison to the FxLMS algorithm plus standard PESQ and STOI scores. No derivation step reduces a claimed prediction or result to its own fitted inputs by construction, no load-bearing self-citation chain is invoked, and no uniqueness theorem or ansatz is smuggled in. The central claims rest on observable empirical differences versus an independent baseline, rendering the work self-contained against external benchmarks.
Axiom & Free-Parameter Ledger
free parameters (2)
- CRN network weights and hyperparameters
- Voice retention loss balancing coefficients
axioms (2)
- domain assumption The Image Source Method produces acoustic impulse responses sufficiently close to real reverberant rooms for training and evaluation.
- domain assumption Complex spectrum mapping combined with LSTM can capture and invert nonlinear acoustic distortions.
Reference graph
Works this paper leans on
-
[1]
C. H. Hansen, Active Noise Control: From Laboratory to Industrial Implementation. London, UK: E & FN Spon, 1997
work page 1997
-
[2]
Active noise control: a tutorial review,
S. M. Kuo and D. R. Morgan, "Active noise control: a tutorial review," Proceedings of the IEEE, vol. 87, no. 6, pp. 943-973, June, 1999
work page 1999
-
[3]
Deep ANC: A deep learning approach to active noise control,
H. Zhang and D. L. Wang, "Deep ANC: A deep learning approach to active noise control," Neural Networks, vol. 141, pp. 1-10, September, 2021
work page 2021
-
[4]
Pyroomacoustics: A Python package for audio room simulation and array processing algorithms,
R. Scheibler, E. Bezzam, and I. Dokmanić, "Pyroomacoustics: A Python package for audio room simulation and array processing algorithms," in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, AB, Canada, pp. 351-355, April, 2018
work page 2018
-
[5]
A. Varga and H. J. Steeneken, "Assessment for automatic speech recognition: II. NOISEX-92: A database and an experiment to study the effect of additive noise on speech recognition systems," Speech Communication, vol. 12, no. 3, pp. 247-251, July, 1993
work page 1993
-
[6]
Librispeech: An ASR corpus based on public domain audio books,
V. Panayotov, G. Chen, D. Povey, and S. Khudanpur, "Librispeech: An ASR corpus based on public domain audio books," in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), South Brisbane, QLD, Australia, pp. 5206-5210, April, 2015
work page 2015
-
[7]
S. J. Elliott, Signal Processing for Active Control. London, UK: Academic Press, 2001. 83
work page 2001
-
[8]
Hybrid FxRLS-FxNLMS Adaptive Algorithm for Active Noise Control in fMRI Application,
R. M. Reddy, I. M. S. Panahi, and R. Briggs, "Hybrid FxRLS-FxNLMS Adaptive Algorithm for Active Noise Control in fMRI Application," IEEE Transactions on Control Systems Technology, vol. 19, no. 2, pp. 474-480, March, 2011
work page 2011
-
[9]
M. T. Akhtar, M. Abe, and M. Kawamata, "A new structure for feedforward active noise control systems with improved online secondary path modeling," IEEE Transactions on Speech and Audio Processing, vol. 13, no. 5, pp. 1082-1088, September, 2005
work page 2005
-
[10]
Recent Advances in Active Noise Control Inside Automobile Cabins: Toward quieter cars,
P. N. Samarasinghe, W. Zhang, and T. D. Abhayapala, "Recent Advances in Active Noise Control Inside Automobile Cabins: Toward quieter cars," IEEE Signal Processing Magazine, vol. 33, no. 6, pp. 61-73, November, 2016
work page 2016
-
[11]
Deep learning for audio signal processing,
H. Purwins, B. Li, T. Virtanen, J. Schlüter, S. Chang, and T. Sainath, "Deep learning for audio signal processing," IEEE Journal of Selected Topics in Signal Processing, vol. 13, no. 2, pp. 206-219, May, 2019
work page 2019
-
[12]
Comparison of neural network architectures for feedforward active control of nonlinear systems,
A. Pike and J. Cheer, "Comparison of neural network architectures for feedforward active control of nonlinear systems," in 2024 Leuven Conference on Noise and Vibration Engineering, Leuven, Belgium, September, 2024
work page 2024
-
[13]
S. Kwon, B.-S. Kim, and J. Park, "Active noise reduction with filtered least-mean-square algorithm improved by long short-term memory models for radiation noise of diesel engine," Applied Sciences, vol. 12, no. 20, pp. 10248, 2022
work page 2022
-
[14]
Deep learning-based active noise control on construction sites,
A. Mostafavi and Y.-J. Cha, "Deep learning-based active noise control on construction sites," Automation in Construction, vol. 151, Art. no. 104885, July 2023. 84
work page 2023
-
[15]
Deep learning-based wind noise prediction study for automotive clay model,
L. Huang, D. Wang, X. Cao, X. Zhang, B. Huang, Y. He, and G. Grabner, "Deep learning-based wind noise prediction study for automotive clay model," Measurement Science and Technology, vol. 35, no. 4, Art. no. 045302, Jan. 2024
work page 2024
-
[16]
ELSTM-ANC-OSPM: Enhanced LSTM in active noise control systems with online secondary path modeling,
Z. Cao, L. Lu, K.-L. Yin, G. Zhu, and B. Chen, "ELSTM-ANC-OSPM: Enhanced LSTM in active noise control systems with online secondary path modeling," IEEE Transactions on Audio, Speech and Language Processing, vol. 33, pp. 4375-4386, 2025
work page 2025
-
[17]
A new hybrid adaptive self-loading FxLMS and CNN-GRU net for active time-varying noise control,
W. Zhu and L. Luo, "A new hybrid adaptive self-loading FxLMS and CNN-GRU net for active time-varying noise control," SSRN preprint, 2024
work page 2024
-
[18]
W. Zhu, Z. Wang, X. Chen, P. Xie, Z. Bai, and L. Luo, "A new adaptive sound zone strategy-based hybrid FxNLMS and CNN-LSTM network for multichannel active noise control in a rehabilitation room," IEEE Sensors Journal, vol. 25, no. 15, pp. 29492-29508, August, 2025
work page 2025
-
[19]
V. D. M. Jabez, A. Ahilan, C. Santhaiah, and V. Thangathurai, "CMANC Net: Fennec fox optimized CNN-BiLSTM network for real time and complex multitude active noise cancellation," Circuits, Systems, and Signal Processing, pp. 1-26, 2025
work page 2025
- [20]
-
[21]
H. Zhang and D. L. Wang, A deep learning approach to active noise control, in Proceedings of Interspeech, Shanghai, China, pp. 1131-1135, October, 2020
work page 2020
-
[22]
Low-Latency Active Noise Control 85 Using Attentive Recurrent Network,
H. Zhang, A. Pandey and D. L. Wang, "Low-Latency Active Noise Control 85 Using Attentive Recurrent Network," in IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 31, pp. 1114-1123, 2023
work page 2023
-
[23]
J. Park, H. H. Cho, H. Lim, and S. W. Lee, "HAD-ANC: A hybrid system comprising an adaptive filter and deep neural networks for active noise control," in Proceedings of Interspeech, Dublin, Ireland, pp. 5321-5325, August, 2023
work page 2023
-
[24]
Neural network-based ANC algorithms: a review,
R. Liu, Q. Liu, Y. Wang, W. Yu, and G. Cheng, "Neural network-based ANC algorithms: a review," Journal of Vibroengineering, vol. 27, no. 6, pp. 1105-1123, Aug. 2025
work page 2025
-
[25]
A comprehensive review on active noise reduction methods for aircraft aerodynamics system,
M. Solanki and A. Dusane, "A comprehensive review on active noise reduction methods for aircraft aerodynamics system," Journal of Vibration Engineering & Technologies, vol. 14, Art. no. 33, January, 2026
work page 2026
-
[26]
A review of artificial intelligence-driven active vibration and noise control,
Z. Jiang, H. Xue, H. Yue, X. Bao, J. Zhu, X. Wang, and L. Zhang, "A review of artificial intelligence-driven active vibration and noise control," Machines, vol. 13, Art. no. 946, October, 2025
work page 2025
-
[27]
Active speech enhancement: Active speech denoising declipping and dereverberation,
O. Yaish, Y. Mishaly, and E. Nachmani, "Active speech enhancement: Active speech denoising declipping and dereverberation," arXiv preprint arXiv:2505.16911, 2025
-
[28]
Deep active speech cancellation with Mamba-masking network,
Y. Mishaly, L. Wolf, and E. Nachmani, "Deep active speech cancellation with Mamba-masking network," arXiv preprint arXiv:2502.01185, 2025
-
[29]
Image method for efficiently simulating small-room acoustics,
J. B. Allen and D. A. Berkley, "Image method for efficiently simulating small-room acoustics," Journal of the Acoustical Society of America, vol. 65, no. 4, pp. 943–950, April, 1979. 86
work page 1979
-
[30]
The performance of adaptive noise cancellation systems in reverberant rooms,
M. H. Lu and P. M. Clarkson, "The performance of adaptive noise cancellation systems in reverberant rooms," The Journal of the Acoustical Society of America, vol. 93, no. 2, pp. 1122-1135, February, 1993
work page 1993
-
[31]
B. Wang, Z. Luo, H. Li, D. Shi, J. Ji, Z. Yang, and W.-S. Gan, "Directional selective fixed-filter active noise control based on a convolutional neural network in reverberant environments," in APSIPA ASC 2025, Singapore, pp. 364-369
work page 2025
-
[32]
Spatially selective active noise control systems,
T. Xiao, B. Xu, and C. Zhao, "Spatially selective active noise control systems," J. Acoust. Soc. Am., vol. 153, pp. 2733-2744, May, 2023
work page 2023
-
[33]
Complex spectral mapping for single- and multi-channel speech enhancement and robust ASR,
Z.-Q. Wang, P. Wang, and D. Wang, "Complex spectral mapping for single- and multi-channel speech enhancement and robust ASR," IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 28, pp. 1778-1787, 2020
work page 2020
-
[34]
DCCRN: Deep complex convolution recurrent network for phase-aware speech enhancement,
Y. Hu, Y. Liu, S. Lv, M. Xing, S. Zhang, Y. Fu, J. Wu, B. Zhang, and L. Xie, "DCCRN: Deep complex convolution recurrent network for phase-aware speech enhancement," in Proc. Interspeech, Shanghai, China, pp. 2472-2476, Oct. 2020
work page 2020
-
[35]
Complex spectral mapping with a convolutional recurrent network for monaural speech enhancement,
K. Tan and D. Wang, "Complex spectral mapping with a convolutional recurrent network for monaural speech enhancement," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), Brighton, UK, pp. 6865-6869, May, 2019
work page 2019
-
[36]
Convolutional neural networks to enhance coded speech,
Z. Zhao, H. Liu, and T. Fingscheidt, "Convolutional neural networks to enhance coded speech," IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 27, no. 4, pp. 663-678, April, 2019
work page 2019
-
[37]
Fast and accurate deep 87 network learning by exponential linear units (ELUs),
D.-A. Clevert, T. Unterthiner, and S. Hochreiter, "Fast and accurate deep 87 network learning by exponential linear units (ELUs)," in Proc. Int. Conf. Learn. Represent. (ICLR), San Juan, Puerto Rico, May, 2016
work page 2016
-
[38]
U-Net: Convolutional networks for biomedical image segmentation,
O. Ronneberger, P. Fischer, and T. Brox, "U-Net: Convolutional networks for biomedical image segmentation," in Proc. Int. Conf. Med. Image Comput. Comput.-Assist. Intervent. (MICCAI), Munich, Germany, pp. 234-241, October, 2015
work page 2015
-
[39]
Adam: A method for stochastic optimization,
D. P. Kingma and J. Ba, "Adam: A method for stochastic optimization," in Proceedings of the International Conference on Learning Representations (ICLR), San Diego, CA, USA, May, 2015
work page 2015
-
[40]
A. W. Rix, J. G. Beerends, M. P. Hollier, and A. P. Hekstra, "Perceptual evaluation of speech quality (PESQ)-a new method for speech quality assessment of telephone networks and codecs," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Salt Lake City, UT, USA, vol. 2, pp. 749-752, May, 2001
work page 2001
-
[41]
An algorithm for intelligibility prediction of time – frequency weighted noisy speech,
C. H. Taal, R. C. Hendriks, R. Heusdens, and J. Jensen, "An algorithm for intelligibility prediction of time – frequency weighted noisy speech," IEEE Transactions on Audio, Speech, and Language Processing, vol. 19, no. 7, pp. 2125-2136, September, 2011
work page 2011
-
[42]
A hybrid SFANC-FxNLMS algorithm for active noise control based on deep learning,
Z. Luo, D. Shi, and W.-S. Gan, “ A hybrid SFANC-FxNLMS algorithm for active noise control based on deep learning,” IEEE Signal Processing Letters, vol. 29, pp. 1102–1106, May, 2022
work page 2022
-
[43]
Z. Luo, D. Shi, J. Ji, X. Shen, and W.-S. Gan, “Real-time implementation and 88 explainable AI analysis of delayless CNN-based selective fixed-filter active noise control,” Mechanical Systems and Signal Processing, vol. 214, pp. 111364, April, 2024
work page 2024
-
[44]
Deep generative fixed-filter active noise control,
Z. Luo, D. Shi, X. Shen, J. Ji, and W.-S. Gan, “ Deep generative fixed-filter active noise control, ” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Rhodes Island, Greece, pp. 1–5, June, 2023
work page 2023
-
[45]
Z. Luo, J. Ji, B. Wang, D. Shi, H. Ma, and W.-S. Gan, “Deep learning-based generative fixed-filter active noise control: Transferability and implementation, ” Mechanical Systems and Signal Processing, vol. 238, pp. 113207, August, 2025
work page 2025
-
[46]
GFANC-Kalman: Generative fixed-filter active noise control with CNN-Kalman filtering,
Z. Luo, D. Shi, X. Shen, J. Ji, and W.-S. Gan, “ GFANC-Kalman: Generative fixed-filter active noise control with CNN-Kalman filtering, ” IEEE Signal Processing Letters, vol. 31, pp. 276–280, January, 2024
work page 2024
-
[47]
Delayless generative fixed-filter active noise control based on deep learning and Bayesian filter,
Z. Luo, D. Shi, W.-S. Gan, and Q. Huang, “ Delayless generative fixed-filter active noise control based on deep learning and Bayesian filter, ” IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 32, pp. 1048–1061, January, 2024
work page 2024
-
[48]
Unsupervised learning based end-to-end delayless generative fixed-filter active noise control,
Z. Luo, D. Shi, X. Shen, and W.-S. Gan, “ Unsupervised learning based end-to-end delayless generative fixed-filter active noise control,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Seoul, Korea, pp. 1–5, April, 2024
work page 2024
-
[49]
GFANC-RL: Reinforcement 89 learning-based generative fixed-filter active noise control,
Z. Luo, H. Ma, D. Shi, and W.-S. Gan, “ GFANC-RL: Reinforcement 89 learning-based generative fixed-filter active noise control,” Neural Networks, vol. 180, pp. 106687, September, 2024
work page 2024
-
[50]
WaveNet-Volterra Neural Network for Active Noise Control: A Fully Causal Approach,
L. Bai, S. Lian, M. Li, Y. He, L. Rao, X. Zeng, R. Sun, K. Chen, and J. Lu, "WaveNet-Volterra Neural Network for Active Noise Control: A Fully Causal Approach," Mechanical Systems and Signal Processing, vol. 241, pp. 113486, December, 2025
work page 2025
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