A Neural Denoising Vocoder for Clean Waveform Generation from Noisy Mel-Spectrogram based on Amplitude and Phase Predictions

Hui-Peng Du; Yang Ai; Ye-Xin Lu; Zhen-Hua Ling

REVIEW 4 major objections 5 minor 18 references

A Neural Denoising Vocoder for Clean Waveform Generation from Noisy Mel-Spectrogram based on Amplitude and Phase Predictions

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A two-stage denoising vocoder generates clean speech directly from noisy mel-spectrograms.

desk verdict A useful mel-only denoising vocoder with a defensible two-stage design; the SOTA claim needs a bigger comparison set and a stated training recipe. read the letter →

arxiv 2411.12268 v1 pith:AXC4JHP3 submitted 2024-11-19 eess.AS eess.SP

Hui-Peng Du , Ye-Xin Lu , Yang Ai , Zhen-Hua Ling This is my paper · ORCID

classification eess.ASeess.SP

keywords neuralvocoderdenoisingspeechenhancementamplitudespectrumpredictionphasemel-spectrograminverseshort-timeFouriertransformVoiceBank+DEMAND

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 claims that a neural vocoder can be turned into a denoising vocoder by splitting the job into two frame-level spectral steps. First, a spectrum predictor reconstructs the noisy amplitude and phase spectra that the input noisy mel-spectrogram has lost. Then an enhancement module cleans those spectra before an inverse short-time Fourier transform rebuilds the waveform. On the VoiceBank+DEMAND test set, the system outperforms two standard neural vocoders, HiFi-GAN and Vocos, and is comparable to two established speech-enhancement models that receive far richer amplitude-spectrum input.

What carries the argument

The load-bearing mechanism is the two-stage cascade in which noisy amplitude and phase spectra serve as an explicit intermediate representation. The first stage, a spectrum predictor adapted from the APNet vocoder, uses separate ResNet-based amplitude and phase predictors to convert the noisy mel-spectrogram into full noisy spectra; the phase predictor matters most because phase information is entirely absent from the mel input. The second stage is the MP-SENet enhancement module, a conformer-based model with separate amplitude-mask and phase decoders that turns the noisy spectra into clean ones, followed by iSTFT to synthesize the waveform. Training the spectrum predictor uses a multi-resolution discriminator and linear anti-wrapping phase losses, while the enhancement module follows its original time-domain, amplitude, complex-spectrum, and anti-wrapping losses with adversarial training.

What would settle it

Ablate the spectrum predictor by feeding the noisy mel-spectrogram straight into the enhancement module and measuring PESQ and STOI on VoiceBank+DEMAND. If the simplified system matches the full pipeline, the claim that noisy spectra must be predicted before enhancement is not supported.

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Extended reading notes

Core claim

The central claim is that clean waveforms can be recovered from a noisy mel-spectrogram by explicitly predicting the noisy amplitude and phase spectra first and then denoising them, rather than asking a single network to jump directly from mel input to clean speech. The authors argue that direct clean-phase recovery from the mel-spectrogram is especially fragile at low SNR because the noisy phase is the clean phase plus an angle term that grows as the noise-to-signal ratio rises. Their two-stage design uses the predicted noisy spectra as a bridge: the spectrum predictor supplies what the mel-spectrogram is missing, and the enhancement module, built on a parallel magnitude-and-phase denoising model, removes the residual noise. Experiments on VoiceBank+DEMAND show the full system reaching a PESQ of 2.88 and STOI of 0.94, surpassing the two vocoder baselines and landing between MetricGAN and MetricGAN+ on the composite quality scores.

Load-bearing premise

The whole pipeline leans on a pre-trained enhancement checkpoint, built for one audio feature configuration, working correctly on the different configuration produced by the spectrum predictor, even though the two stages were never jointly trained or explicitly aligned.

Editorial extensions

If this is right

A vocoder that accepts only mel-spectrograms can perform denoising, so noisy speech from a target speaker can be converted to clean synthesis without requiring a separate waveform-enhancement front end.
Predicting noisy spectra as an intermediate beats trying to predict clean spectra directly, especially for phase recovery in low-SNR conditions.
Off-the-shelf speech-enhancement models can be recycled as the second stage of a denoising vocoder, suggesting a modular route to other vocoder–enhancer combinations.
The system reaches the quality level of amplitude-input speech-enhancement models despite operating from a lossy mel-spectrogram, setting a practical baseline for mel-only denoising.

Reading between the lines

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

Because the enhancement module is used as a frozen checkpoint with different STFT settings from the spectrum predictor, the reported gains may partly reflect how well that checkpoint generalizes across feature configurations; a version fine-tuned end-to-end on the bridge features would separate this transfer effect from the architecture's benefit.
The same two-stage bridge could be tested with other lossy acoustic inputs, such as speaker embeddings or noise-robust features, or with other enhancement backbones, to see whether the noisy-spectrum bridge is the general principle.
The phase-only angle equation suggests a direct extension: a predictor that estimates the noise-to-signal ratio per time-frequency bin could let the system condition its denoising on expected phase deviation, potentially improving very-low-SNR cases.

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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

The new thing here is a mel-only denoising vocoder: the spectrum predictor converts the noisy mel into noisy amplitude/phase, and MP-SENet cleans those spectra before iSTFT. That removes the F0 requirement of the earlier DNR-HiNet, which is a real step forward for noisy TTS and VC pipelines. The paper is honest about what it does and does not achieve — it positions the method as comparable to, not better than, the SE baselines on several metrics, and the ablation in Table 3 actually defends the STFT mismatch, since forcing the spectrum predictor to match MP-SENet's STFT parameters drops PESQ from 2.88 to 2.26. I think the stress-test note has the right emphasis: the STFT concern is largely answered by the paper itself, and the load-bearing gap is the comparison set and the training protocol.

What the paper does well: the architecture is clean, the equation motivating the phase bridge is a true identity, and the ablations are informative. The reported gains over HiFi-GAN and Vocos, modified to take noisy mel input, are consistent across all six metrics. The audio demo page is a good touch, and the paper does not oversell its SE comparison.

The soft spots, in proportion: first, the "state-of-the-art performance compared to existing neural vocoders" claim rests on exactly two baselines, and DNR-HiNet — the closest prior denoising vocoder — is cited but never evaluated. That is the main hole. Second, no error bars or significance tests, so "significantly outperformed" is just a word. Third, the MP-SENet training recipe is genuinely ambiguous: the paper says it uses the open-source checkpoint, but also says training all models ran for 700k steps with a 2e-4 learning rate. Readers cannot tell whether MP-SENet is frozen, fine-tuned, or co-trained. That matters because the cascade's performance could depend on how much adaptation happens. None of these flaws are fatal — the contribution is a plausible engineering result — but they keep the strongest claims from being fully established.

Who this is for: people working on noise-robust TTS or voice conversion who want a vocoder that runs from mel alone, and anyone building on APNet/MP-SENet-style spectral pipelines. The paper deserves a serious referee: the idea is novel enough and the evidence is suggestive enough to warrant a careful look, with the expectation that the authors tighten the comparison and clarify the training protocol before acceptance.

Referee Report

4 major / 5 minor

Summary. The paper proposes a neural denoising vocoder that maps a noisy mel-spectrogram to a clean waveform in two stages. A spectrum predictor (an APNet-derived module with separate amplitude and phase predictors) first estimates the noisy amplitude and phase spectra from the noisy mel-spectrogram; an enhancement module (MP-SENet) then denoises these spectra; the clean waveform is reconstructed by iSTFT. Experiments on VoiceBank+DEMAND compare against HiFi-GAN and Vocos as vocoder baselines and against MetricGAN/MetricGAN+ as speech-enhancement baselines, with additional ablations that replace the spectrum predictor with the original APNet and that match the STFT configuration of MP-SENet. The paper claims state-of-the-art performance among neural vocoders and performance comparable to several speech-enhancement methods.

Significance. If the results hold, the paper demonstrates that a mel-only denoising vocoder is practical and that a two-stage spectral bridge (noisy amplitude/phase prediction followed by spectral enhancement) is an effective design. The work builds on existing components (APNet and MP-SENet) and is clearly motivated by real noisy TTS scenarios. The paper includes a useful ablation: Table 3 shows that deliberately matching the STFT configuration of MP-SENet degrades PESQ from 2.88 to 2.26, which is an empirical defense of the mismatched-configuration design. Equation (1) is a true identity and is used only as motivation, so there is no circularity in the evaluation. The main weaknesses are in the evaluation protocol: the SOTA claim rests on only two vocoder baselines, no significance testing accompanies the metric comparisons, and the training/fine-tuning status of MP-SENet is ambiguous.

major comments (4)

[Section 3.2, Table 1] The central claim of state-of-the-art performance among neural vocoders is supported only by comparison with HiFi-GAN and Vocos, both of which are standard clean-speech vocoders that the paper modifies by training them on noisy mel-spectrograms. The manuscript itself identifies DNR-HiNet [7] as the closest prior denoising vocoder, but DNR-HiNet is never evaluated. A SOTA claim requires either an evaluation against the most relevant existing denoising vocoder or an explicit and justified statement of why that comparison is excluded. As written, the claim overreaches the evidence.
[Section 3.1, Implementation] The manuscript does not specify whether the open-source MP-SENet checkpoint is kept frozen, fine-tuned, or jointly trained with the spectrum predictor during the 700k training steps. The text says both 'we use the open source checkpoint of MP-SENet' and 'Training of all models employed AdamW ... for 700k steps,' which is ambiguous. This is load-bearing because the enhancement module receives spectra computed with a 1024-point FFT that differ from the 400-point FFT configuration used when the MP-SENet checkpoint was trained, and the behavior of the cascade depends critically on whether the enhancement module is adapted to this input distribution. Please state explicitly which parameters are updated in each training stage.
[Section 3.2, Tables 1-3] All objective metrics are reported as point estimates on a single test set, without confidence intervals, significance tests, or multiple training runs. The word 'significantly' in Section 3.2 is therefore not statistically supported. While the gaps over HiFi-GAN and Vocos appear large, the comparison with MetricGAN+ in Table 2 is close (e.g., PESQ 2.88 vs 3.15, CBAK 3.06 vs 3.16), and the claim of 'comparable' performance cannot be assessed without error bars. The authors should report variance or significance, or at minimum temper the language of 'significantly.'
[Section 3.3, Table 2] The speech-enhancement comparisons are limited to MetricGAN (2019) and MetricGAN+ (2021), which are not representative of current state-of-the-art SE systems. The abstract's claim of 'comparable performance with the serveral advanced speech enhancement methods' is therefore weakened, since the selected baselines are more than three years old and are amplitude-only methods. Either update the SE baseline set to more recent methods or narrow the claim to 'comparable to the evaluated SE methods.'

minor comments (5)

[Abstract, Section 2.1, Section 3.1] There are several typos: 'serveral' in the abstract, 'spectrum predictior' in Section 2.1, 'metircs' in Section 3.1, 'T able' in table captions, 'SE filed' in Section 2.3, and 'MeticGAN+' in Section 3.3.
[Section 3.1, Implementation] Training details are incomplete: the manuscript gives the learning rate and number of steps but not the learning-rate schedule, batch size, number of GPUs, or whether the spectrum predictor and enhancement module are trained separately or jointly. These details are needed for reproducibility.
[Section 3.4, Table 3] The STFT-mismatch ablation is commendable and directly addresses a likely reviewer concern, but it is also a single-run point estimate. Reporting variance or a small number of runs would make the conclusion that the mismatched configuration is preferable more robust.
[Section 3.3, Table 2] Table 2 omits SSNR and STOI because the original MetricGAN papers did not report them, but these metrics are standard on VoiceBank+DEMAND. If released checkpoints are available, computing them for MetricGAN/MetricGAN+ would provide a more complete comparison; otherwise the omission should be noted in the table caption.
[Section 2.3] The enhancement module is described as using MP-SENet with Conformer blocks, amplitude mask decoder, and phase decoder. A few sentences on how the phase decoder is trained (e.g., the anti-wrapping loss) would help readers who do not know MP-SENet.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claim rests on held-out evaluation against external baselines, not on the paper's own construction.

full rationale

The paper's derivation chain is not circular. Eq. (1) is a standard trigonometric identity used only to motivate the need for phase prediction in low-SNR conditions; it is not used to derive the claimed results. The proposed system is a cascade of a spectrum predictor (modified from APNet) and an enhancement module (MP-SENet), and its performance is measured on the held-out VoiceBank+DEMAND test set against external baselines (HiFi-GAN, Vocos, MetricGAN, MetricGAN+). The self-citations to APNet, APNet2, and MP-SENet are dependencies on prior systems, but those systems are externally published artifacts with their own training and evaluations; invoking them does not make the benchmark numbers equivalent to the paper's inputs. The STFT configuration mismatch between the two stages is explicitly investigated in Table 3, where the paper reports that matching MP-SENet's STFT settings degrades performance (PESQ drops from 2.88 to 2.26), so the design choice is empirically defended rather than assumed. Concerns about the limited number of vocoder baselines, missing significance tests, and ambiguity about whether MP-SENet is frozen or fine-tuned are legitimate scientific-quality concerns, but they are not circularity: the predictions are not fitted to the test set, and no claim reduces by construction to a fitted parameter or to an unverified self-citation.

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

The physics and signal processing content is minimal: Eq. (1) is a standard identity for the phase of a sum of two complex numbers. The novel contribution is an empirical system, so the ledger captures the assumptions that the system's performance depends on: the sufficiency of mel-spectrograms for spectrum recovery, transfer of the pretrained MP-SENet checkpoint, and the reliability of objective metrics as quality proxies. No new entities are introduced.

free parameters (3)

Initial learning rate = 0.0002
AdamW learning rate chosen by hand and reported in Section 3.1; no tuning or sensitivity analysis is given.
Training duration = 700k steps
Reported as a fixed training budget; no convergence criterion is stated, so early stopping or overfitting is not assessed.
STFT configurations = 1024/320/80 for predictor; 400/400/100 for enhancer
Section 3.4 shows the exact configuration affects results (matching STFT hurts performance), so these hand-picked settings matter to the reported numbers.

assumptions (4)

domain assumption The 80-dimensional mel-spectrogram retains enough spectral detail to recover usable noisy full-band amplitude and phase spectra.
The entire pipeline depends on ASP and PSP being able to invert the mel compression and the absence of phase; supported only by the final empirical results, not proven.
standard math The additive noise phase relation in Eq. (1) is the standard identity for complex-valued speech plus noise.
This is true by the definition of complex addition; used to motivate phase prediction.
domain assumption MP-SENet's pretrained checkpoint transfers to the spectral representations produced by the spectrum predictor.
Section 3.1 says the open-source checkpoint is used; if the checkpoint is not fine-tuned, this transfer assumption is load-bearing and untested.
domain assumption Objective metrics (PESQ, CSIG, CBAK, COVL, SSNR, STOI) are sufficient proxies for perceptual speech quality.
No listening test is reported; conclusions rely on these metrics.

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Cite this review

Pith. "Pith review of A Neural Denoising Vocoder for Clean Waveform Generation from Noisy Mel-Spectrogram based on Amplitude and Phase Predictions." pith.science (2026). https://pith.science/paper/AXC4JHP3

@misc{pith2026241112268,
  author       = {Pith},
  title        = {Pith review of: A Neural Denoising Vocoder for Clean Waveform Generation from Noisy Mel-Spectrogram based on Amplitude and Phase Predictions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AXC4JHP3}},
  note         = {Machine review of arXiv:2411.12268}
}

read the original abstract

This paper proposes a novel neural denoising vocoder that can generate clean speech waveforms from noisy mel-spectrograms. The proposed neural denoising vocoder consists of two components, i.e., a spectrum predictor and a enhancement module. The spectrum predictor first predicts the noisy amplitude and phase spectra from the input noisy mel-spectrogram, and subsequently the enhancement module recovers the clean amplitude and phase spectrum from noisy ones. Finally, clean speech waveforms are reconstructed through inverse short-time Fourier transform (iSTFT). All operations are performed at the frame-level spectral domain, with the APNet vocoder and MP-SENet speech enhancement model used as the backbones for the two components, respectively. Experimental results demonstrate that our proposed neural denoising vocoder achieves state-of-the-art performance compared to existing neural vocoders on the VoiceBank+DEMAND dataset. Additionally, despite the lack of phase information and partial amplitude information in the input mel-spectrogram, the proposed neural denoising vocoder still achieves comparable performance with the serveral advanced speech enhancement methods.

Figures

Figures reproduced from arXiv: 2411.12268 by the authors.

**Figure 1.** Overall architecture of the proposed neural denoising vocoder. Here, ASP, PSP, and iSTFT stand for amplitude spectrum predictor, phase spectrum predictor, and inverse short-time Fourier transform, respectively. amplitude spectrum and phase spectrum from the noisy mel-spectrogram. In the enhancement module, the SE model denoises the predicted noisy amplitude and phase spectra to clean ones. Finally, the clean speech … view at source ↗

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Reference graph

Works this paper leans on

18 extracted references · 17 canonical work pages

[7]

IEEE/ACM Transac- tions on Audio, Speech, and Language Processing30, 2036–2048 (2022)

Ai, Y., Ling, Z.H., Wu, W.L., Li, A.: Denoising-and-dereverberation hierarchical neural vocoder for statistical parametric speech synthesis. IEEE/ACM Transac- tions on Audio, Speech, and Language Processing30, 2036–2048 (2022)

work page 2022
[1]

Kong, J., Kim, J., Bae, J.: HiFi-GAN: Generative adversarial networks for efficient and high fidelity speech synthesis. Proc. NeurIPS33, 17022–17033 (2020)

work page 2020
[2]

arXiv preprint arXiv:2306.00814 (2023)

Siuzdak, H.: Vocos: Closing the gap between time-domain and fourier-based neural vocoders for high-quality audio synthesis. arXiv preprint arXiv:2306.00814 (2023)

arXiv 2023
[3]

IEEE/ACM Transactions on Audio, Speech, and Language Processing 26(8), 1420–1433 (2018)

Valentini-Botinhao, C., Yamagishi, J.: Speech enhancement of noisy and reverber- ant speech for text-to-speech. IEEE/ACM Transactions on Audio, Speech, and Language Processing 26(8), 1420–1433 (2018)

work page 2018
[4]

In: Proc

Ai, Y., Zhang, J.X., Chen, L., Ling, Z.H.: Dnn-based spectral enhancement for neural waveform generators with low-bit quantization. In: Proc. ICASSP. pp. 7025– 7029 (2019)

work page 2019
[5]

In: Proc

Pascual, S., Bonafonte, A., Serrà, J.: SEGAN: Speech enhancement generative adversarial network. In: Proc. Interspeech. pp. 3642–3646 (2017)

work page 2017
[6]

In: Proc

Défossez,A.,Synnaeve,G.,Adi,Y.:Realtimespeechenhancementinthewaveform domain. In: Proc. Interspeech. pp. 3291–3295 (2020)

work page 2020
[8]

IEEE/ACM Transactions on Audio, Speech, and Language Processing (2023)

Ai, Y., Ling, Z.H.: APNet: An all-frame-level neural vocoder incorporating direct prediction of amplitude and phase spectra. IEEE/ACM Transactions on Audio, Speech, and Language Processing (2023)

work page 2023

Show all 18 references

[9]

In: Proc

Lu,Y.X.,Ai,Y.,Ling,Z.H.:MP-SENet:Aspeechenhancementmodelwithparallel denoising of magnitude and phase spectra. In: Proc. Interspeech. pp. 3834–3838 (2023)

2023
[10]

In: Proc

Du, H.P., Lu, Y.X., Ai, Y., Ling, Z.H.: APNet2: High-quality and high-efficiency neural vocoder with direct prediction of amplitude and phase spectra. In: Proc. NCMMSC. pp. 66–80 (2023)

2023
[11]

In: Proc

Ai, Y., Ling, Z.H.: Neural speech phase prediction based on parallel estimation architecture and anti-wrapping losses. In: Proc. ICASSP. pp. 1–5 (2023)

2023
[12]

In: Proc

Woo, S., Debnath, S., Hu, R., Chen, X., Liu, Z., Kweon, I.S., Xie, S.: ConvNeXt v2: Co-designing and scaling convnets with masked autoencoders. In: Proc. CVPR. pp. 16133–16142 (2023)

2023
[13]

In: Proc

Fu, S.W., Liao, C.F., Tsao, Y., Lin, S.D.: MetricGAN: Generative Adversarial Networks Based Black-Box Metric Scores Optimization for Speech Enhancement. In: Proc. ICML. pp. 2031–2041 (2019)

2019
[14]

In: Proc

Valentini-Botinhao, C., Wang, X., Takaki, S., Yamagishi, J.: Investigating rnn- based speech enhancement methods for noise-robust text-to-speech. In: Proc. SSW. pp. 146–152 (2016)

2016
[15]

In: Proc

Veaux, C., Yamagishi, J., King, S.: The voice bank corpus: Design, collection and data analysis of a large regional accent speech database. In: Proc. O- COCOSDA/CASLRE. pp. 1–4 (2013)

2013
[16]

In: Proc

Thiemann, J., Ito, N., Vincent, E.: The diverse environments multi-channel acous- tic noise database (DEMAND): A database of multichannel environmental noise recordings. In: Proc. ICA. vol. 19, p. 035081 (2013)

2013
[17]

In: Proc

Loshchilov, I., Hutter, F.: Decoupled weight decay regularization. In: Proc. ICLR (2018)

2018
[18]

In: Proc

Fu, S.W., Yu, C., Hsieh, T.A., Plantinga, P., Ravanelli, M., Lu, X., Tsao, Y.: MetricGAN+: An Improved Version of MetricGAN for Speech Enhancement. In: Proc. Interspeech. pp. 201–205 (2021)

2021

Pith tools

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

[1] [7]

IEEE/ACM Transac- tions on Audio, Speech, and Language Processing30, 2036–2048 (2022)

Ai, Y., Ling, Z.H., Wu, W.L., Li, A.: Denoising-and-dereverberation hierarchical neural vocoder for statistical parametric speech synthesis. IEEE/ACM Transac- tions on Audio, Speech, and Language Processing30, 2036–2048 (2022)

work page 2022

[2] [1]

Kong, J., Kim, J., Bae, J.: HiFi-GAN: Generative adversarial networks for efficient and high fidelity speech synthesis. Proc. NeurIPS33, 17022–17033 (2020)

work page 2020

[3] [2]

arXiv preprint arXiv:2306.00814 (2023)

Siuzdak, H.: Vocos: Closing the gap between time-domain and fourier-based neural vocoders for high-quality audio synthesis. arXiv preprint arXiv:2306.00814 (2023)

arXiv 2023

[4] [3]

IEEE/ACM Transactions on Audio, Speech, and Language Processing 26(8), 1420–1433 (2018)

Valentini-Botinhao, C., Yamagishi, J.: Speech enhancement of noisy and reverber- ant speech for text-to-speech. IEEE/ACM Transactions on Audio, Speech, and Language Processing 26(8), 1420–1433 (2018)

work page 2018

[5] [4]

In: Proc

Ai, Y., Zhang, J.X., Chen, L., Ling, Z.H.: Dnn-based spectral enhancement for neural waveform generators with low-bit quantization. In: Proc. ICASSP. pp. 7025– 7029 (2019)

work page 2019

[6] [5]

In: Proc

Pascual, S., Bonafonte, A., Serrà, J.: SEGAN: Speech enhancement generative adversarial network. In: Proc. Interspeech. pp. 3642–3646 (2017)

work page 2017

[7] [6]

In: Proc

Défossez,A.,Synnaeve,G.,Adi,Y.:Realtimespeechenhancementinthewaveform domain. In: Proc. Interspeech. pp. 3291–3295 (2020)

work page 2020

[8] [8]

IEEE/ACM Transactions on Audio, Speech, and Language Processing (2023)

Ai, Y., Ling, Z.H.: APNet: An all-frame-level neural vocoder incorporating direct prediction of amplitude and phase spectra. IEEE/ACM Transactions on Audio, Speech, and Language Processing (2023)

work page 2023