pith. sign in

arxiv: 2606.23665 · v1 · pith:4FC4IBLYnew · submitted 2026-06-22 · 📡 eess.AS · cs.CV

PHAST-Net: Attention-Guided, Physics-Informed Network for Unified Estimation of Ideal Time-Frequency Representations

James M. Cozens , Simon J. Godsill This is my paper

Pith reviewed 2026-06-26 06:33 UTC · model grok-4.3

classification 📡 eess.AS cs.CV
keywords PHAST-Nettime-frequency representationswavelet transformsphysics-informed neural networkattention mechanismsspeech analysismusic analysisnonstationary signals
0
0 comments X

The pith

PHAST-Net learns a mapping from a selected constellation of wavelet transforms to high-resolution ideal time-frequency representations using attention and a physics-informed reprojection loss.

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

The paper introduces PHAST-Net to estimate ideal time-frequency representations such as spectrograms, tempograms, and metrograms from a constellation of continuous log-frequency adaptive wavelet transforms. The constellation is chosen via Cohen's class kernel analysis to cover curvature in a log-frequency plane suited to harmonic signals, and the network uses attention for cross-term suppression plus an auxiliary loss that reprojects the output back onto the input transforms. This setup aims to deliver a single framework that handles spectral, tempo-based, metrical, and harmonic representations while enforcing energy conservation and consistency during training on procedurally generated data. A reader would care because existing methods often require separate tools for each representation type and struggle with cross-terms in nonstationary signals like speech and music.

Core claim

PHAST-Net estimates ITFRs by learning an application-general mapping from the proposed CLAWT constellation to high-resolution, cross-term-suppressed representations; the mapping is guided by attention layers and regularized by a physics-informed auxiliary reprojection loss that reconstructs the observed CLAWTs from the predicted ITFR and the corresponding Cohen's class kernels. The log-frequency formulation supports a Harmonic variant that isolates fundamental structure, while a Spline variant parameterizes detected ridges as continuous trajectories. Trained on an unbounded procedural dataset, the approach yields improved accuracy over established methods for unified analysis of speech, musi

What carries the argument

The physics-informed auxiliary reprojection loss that reconstructs the input CLAWT constellation from the predicted ITFR using the corresponding Cohen's class kernels, combined with attention layers for cross-term suppression.

If this is right

  • A single trained network supplies spectral, tempo, metrical, and harmonic representations without separate estimators for each.
  • The harmonic variant isolates fundamental structure and supports derived fundamental tempograms and metrograms.
  • The spline variant converts detected ridges into continuous trajectories that support arbitrary-grid re-rendering and signal reconstruction.
  • The reprojection loss reduces target sparsity effects and improves training stability while preserving energy conservation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The log-frequency formulation might transfer to other harmonic-rich signals such as certain biomedical or mechanical recordings if the curvature-coverage selection still applies.
  • The unified mapping could reduce the need for hand-tuned kernel parameters in conventional Cohen's class methods when the network is retrained on domain-specific data.
  • If the reprojection loss proves robust, similar consistency objectives might be added to other physics-informed networks that map between related signal representations.

Load-bearing premise

The procedurally generated dataset and the CLAWT constellation selected by Cohen's class analysis produce inputs and targets that generalize to real nonstationary signals without introducing biases from the synthetic generation process.

What would settle it

Evaluating PHAST-Net accuracy on a large collection of real recorded speech and music signals against both traditional TFR methods and the reported synthetic-test performance would show whether the claimed improvements persist outside the procedural data.

Figures

Figures reproduced from arXiv: 2606.23665 by James M. Cozens, Simon J. Godsill.

Figure 1
Figure 1. Figure 1: PHAST-Net Architecture (I = 1024) yn ∈ R K×H×W is the K-channel physics target tensor, generated from yn = P(xn). The proposed loss function is then given by: Ltotal = Lx,mse + Lx,log + Ly,mse + Ly,log + LT V , (15) The MSE Image Reconstruction Loss, Lx,mse, is the mean squared error between the predicted and ground truth ITFRs: Lx,mse = λx,mse NHW XN n=1 ∥xn−ˆxn∥ 2 F , where ˆxn = fΘ (Φn) and ∥X∥ 2 F deno… view at source ↗
Figure 2
Figure 2. Figure 2: Block diagram representing the PHAST-Net training process [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: A visualisation of the PHAST-Net framework applied to a speech excerpt from the “Harvard sentences” database [76]. On the left, the action of the [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A visualisation of the PHAST-Net framework applied to a short violin extract from the piece “Piano Concerto No. 4” by the author. As per the speech [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: A visualisation of the PHAST-Net framework applied to the evaluative signal [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: A visualisation of the Fundamental Tempogram and Metrogram inference process: (a) provides the reference ITFR for the simulated musical excerpt, [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparative evaluation on the multi-component benchmark of Eq. (44) with additive white Gaussian noise (AWGN) at an SNR of [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Example procedurally generated input data point, comprising a randomly generated tonal ITFR target in Panel (f), the corresponding harmonic ITFR [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
read the original abstract

We introduce PHAST-Net, an attention-guided, physics-informed network for unified estimation of Ideal Time-Frequency Representations (ITFRs), spanning spectral, tempo-based, metrical, and harmonic representations such as Spectrograms, Tempograms, and Metrograms. PHAST-Net learns an application-general mapping from a constellation of wavelet transforms, the proposed Continuous Log-frequency Adaptive Wavelet Transform (CLAWT), to high-resolution, cross-term-suppressed time-frequency (T-F) representations. The proposed constellation of CLAWTs is selected through Cohen's class kernel analysis to maximise curvature coverage in a logarithmic-frequency T-F plane tailored to harmonic signal structure. PHAST-Net further incorporates a proposed physics-informed auxiliary reprojection loss designed to reconstruct the idealised observed CLAWT constellation from the predicted ITFR and the corresponding Cohen's class kernels during training. This auxiliary objective promotes transform consistency and energy conservation, mitigates pathological target sparsity, and enhances optimisation stability. Attention layers further promote effective cross-term suppression across the input constellation. The log-frequency formulation also enables Harmonic PHAST-Net, which estimates a Harmonic ITFR that isolates fundamental structure, supporting robust fundamental-only representations for speech and music, such as derived fundamental Tempograms and Metrograms. We further introduce Spline-PHAST-Net, which parameterises detected and associated T-F ridges as continuous spline trajectories, enabling arbitrary-grid re-rendering and signal reconstruction. Trained on an effectively unbounded procedurally generated dataset, PHAST-Net demonstrates improved accuracy over established approaches, providing a unified framework for high-resolution, cross-term-robust analysis of speech, music, and broader nonstationary signals.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper introduces PHAST-Net, an attention-guided physics-informed neural network that maps a Cohen's-class-selected constellation of Continuous Log-frequency Adaptive Wavelet Transforms (CLAWTs) to high-resolution, cross-term-suppressed Ideal Time-Frequency Representations (ITFRs) including spectrograms, tempograms, and metrograms. It incorporates an auxiliary reprojection loss to enforce consistency between the predicted ITFR and the input CLAWTs via the corresponding kernels, uses attention for cross-term suppression, and introduces variants such as Harmonic PHAST-Net and Spline-PHAST-Net. The network is trained exclusively on an unbounded procedurally generated dataset and is claimed to outperform established approaches for speech, music, and nonstationary signals.

Significance. If the central claims hold after proper validation, the work could provide a unified, high-resolution framework for T-F analysis of harmonic signals with built-in cross-term robustness and energy conservation, potentially useful for downstream tasks in audio processing. The physics-informed reprojection loss and log-frequency formulation are conceptually attractive strengths, but their practical impact cannot be assessed without quantitative evidence.

major comments (3)
  1. [Abstract] Abstract: the central claim of 'improved accuracy over established approaches' is stated without any quantitative metrics, baselines, error bars, statistical tests, or dataset details; this absence makes the claim impossible to evaluate and is load-bearing for the paper's contribution.
  2. [Abstract] Abstract: training occurs exclusively on procedurally generated data whose statistics are controlled by the synthetic prior, yet no experiments, ablation, or discussion address generalization to real recordings (e.g., natural speech or music with differing modulation, noise, or harmonic statistics); this is the load-bearing assumption for applicability claims.
  3. [Abstract] Abstract: the reprojection loss is described as promoting 'transform consistency and energy conservation,' but no equations are supplied showing whether the loss is independent of the network parameters or reduces to a self-referential term that could be satisfied by construction; this risks circularity in the optimization objective.
minor comments (1)
  1. [Abstract] The abstract introduces several new terms (CLAWT, ITFRs, Harmonic PHAST-Net, Spline-PHAST-Net) without a concise definition or reference to their first appearance in the main text.

Simulated Author's Rebuttal

3 responses · 0 unresolved

Thank you for the referee's constructive comments on the manuscript. We address each major comment point-by-point below, indicating planned revisions to improve clarity and evaluability without altering the core contributions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim of 'improved accuracy over established approaches' is stated without any quantitative metrics, baselines, error bars, statistical tests, or dataset details; this absence makes the claim impossible to evaluate and is load-bearing for the paper's contribution.

    Authors: The abstract is a high-level summary; the full manuscript provides quantitative comparisons against baselines (including error bars and statistical tests) along with dataset details in the Experiments section. To address the concern directly in the abstract, we will revise it to include key performance metrics and a brief description of the evaluation setup. revision: yes

  2. Referee: [Abstract] Abstract: training occurs exclusively on procedurally generated data whose statistics are controlled by the synthetic prior, yet no experiments, ablation, or discussion address generalization to real recordings (e.g., natural speech or music with differing modulation, noise, or harmonic statistics); this is the load-bearing assumption for applicability claims.

    Authors: The manuscript prioritizes the unbounded procedural dataset to enable controlled and comprehensive training. We will add a discussion subsection addressing the design choices in the synthetic prior intended to support generalization and note limitations regarding direct validation on real recordings as an area for future work. revision: partial

  3. Referee: [Abstract] Abstract: the reprojection loss is described as promoting 'transform consistency and energy conservation,' but no equations are supplied showing whether the loss is independent of the network parameters or reduces to a self-referential term that could be satisfied by construction; this risks circularity in the optimization objective.

    Authors: The full manuscript supplies the mathematical definition of the reprojection loss (as the discrepancy between input CLAWTs and kernel-reprojected predictions from the estimated ITFR), which is independent of network parameters and enforces consistency rather than being trivially satisfiable. We will revise the abstract to reference the loss formulation and clarify its auxiliary, non-circular nature. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper presents PHAST-Net as a neural network trained on procedurally generated synthetic data to map a CLAWT constellation (selected via standard Cohen's class analysis) to target ITFRs, using an auxiliary reprojection loss for consistency. No quoted equations or descriptions show any prediction reducing by construction to fitted inputs, self-definitional targets, or load-bearing self-citations. The central claims rest on empirical accuracy improvements over baselines within the described training setup, which is externally falsifiable and does not collapse to renaming or tautological reparameterization. This is the expected non-finding for a data-driven architecture paper.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

Based on abstract only; the central claim rests on domain assumptions about wavelet transforms and synthetic data representing real signals, plus the new proposed entities CLAWT and ITFRs whose independent validation is not shown.

axioms (2)
  • domain assumption Cohen's class kernel analysis selects a CLAWT constellation that maximises curvature coverage for harmonic signals
    Stated in abstract as the selection method for the input transforms.
  • domain assumption The physics-informed auxiliary reprojection loss mitigates target sparsity and enhances optimisation stability
    Claimed benefit of the loss in the abstract without derivation details.
invented entities (2)
  • CLAWT (Continuous Log-frequency Adaptive Wavelet Transform) no independent evidence
    purpose: Constellation of input wavelet transforms tailored to harmonic structure
    New transform proposed in the paper; no independent evidence provided in abstract.
  • Ideal Time-Frequency Representations (ITFRs) no independent evidence
    purpose: High-resolution, cross-term-suppressed target representations
    Core target concept introduced; no external validation shown.

pith-pipeline@v0.9.1-grok · 5834 in / 1349 out tokens · 26047 ms · 2026-06-26T06:33:04.778617+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

75 extracted references · 4 canonical work pages

  1. [1]

    Dakovic, L

    M. Dakovic, L. Stankovic, and T. Thayaparan,Time-Frequency Signal Analysis with Applications. Norwood, MA, USA: Artech House, 2013

    2013

  2. [2]

    Boashash,Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, 2nd ed

    B. Boashash,Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, 2nd ed. Academic Press, 2015

    2015

  3. [3]

    The applied principles of EEG analysis methods in neuroscience and clinical neurology,

    H. Zhang, Q. Q. Zhou, H. Chen, et al., “The applied principles of EEG analysis methods in neuroscience and clinical neurology,”Military Medical Research, vol. 10, no. 1, Art. no. 67, 2023

    2023

  4. [4]

    Performance evaluation of time–frequency distributions for ECG signal analysis,

    A. F. Hussein, S. J. Hashim, A. F. A. Aziz, et al., “Performance evaluation of time–frequency distributions for ECG signal analysis,”Journal of Medical Systems, vol. 42, no. 1, Art. no. 15, 2018

    2018

  5. [5]

    EEG-based emotion recognition using quadratic time–frequency distribution,

    R. Alazrai, R. Homoud, H. Alwanni, and M. I. Daoud, “EEG-based emotion recognition using quadratic time–frequency distribution,”Sensors, vol. 18, no. 8, Art. no. 2739, 2018

    2018

  6. [6]

    A guide to LIGO–Virgo detector noise and extraction of transient gravitational-wave signals,

    The LIGO Scientific Collaboration and the Virgo Collaboration, “A guide to LIGO–Virgo detector noise and extraction of transient gravitational-wave signals,” Classical and Quantum Gravity, vol. 37, no. 5, art. no. 055002, Feb. 2020

    2020

  7. [8]

    Available: https://arxiv.org/abs/2501.15764

    [Online]. Available: https://arxiv.org/abs/2501.15764

    arXiv

  8. [9]

    Cyclic tempogram—A mid-level tempo representation for music signals,

    P. Grosche, M. M ¨uller, and F. Kurth, “Cyclic tempogram—A mid-level tempo representation for music signals,” in2010 IEEE International Conference on Acoustics, Speech and Signal Processing, Dallas, TX, USA, 2010, pp. 5522–5525

    2010

  9. [10]

    Time Variable Tempo Detection and Beat Marking,

    G. Peeters, “Time Variable Tempo Detection and Beat Marking,” inProc. Int. Comput. Music Conf. (ICMC), Barcelona, Spain, 2005, pp. 539–542

    2005

  10. [11]

    Novel characterization method of impedance cardiography signals using time–frequency distributions,

    J. Escriv ´a Mu ˜noz, Y . Pan, S. Ge, E. W. Jensen, and M. Vallverd ´u, “Novel characterization method of impedance cardiography signals using time–frequency distributions,”Medical and Biological Engineering and Computing, vol. 56, no. 10, pp. 1757–1770, 2018. 11 440 880 1.8k 3.5kFrequency (Hz) 0 2.5 5 7.5 10 Time (s) 440 880 1.8k 3.5kFrequency (Hz) 0 2.5...

    2018

  11. [12]

    Recent advances in time–frequency analysis methods for machinery fault diagnosis: A review with application examples,

    Z. Feng, M. Liang, and F. Chu, “Recent advances in time–frequency analysis methods for machinery fault diagnosis: A review with application examples,” Mechanical Systems and Signal Processing, vol. 38, no. 1, pp. 165–205, 2013

    2013

  12. [13]

    Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis,

    C.-Y . Lin, L. Su, and H.-T. Wu, “Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis,”J. F ourier Anal. Appl., vol. 24, no. 2, pp. 451– 505, 2018

    2018

  13. [14]

    A signal-dependent time–frequency represen- tation: Optimal kernel design,

    R. G. Baraniuk and D. L. Jones, “A signal-dependent time–frequency represen- tation: Optimal kernel design,”IEEE Transactions on Signal Processing, vol. 41, no. 4, pp. 1589–1602, 1993

    1993

  14. [15]

    An adaptive optimal-kernel time–frequency representation,

    D. L. Jones and R. G. Baraniuk, “An adaptive optimal-kernel time–frequency representation,”IEEE Transactions on Signal Processing, vol. 43, no. 10, pp. 2361– 2371, 1995

    1995

  15. [16]

    Locally optimized adaptive directional time–frequency distributions,

    M. Mohammadi, A. A. Pouyan, N. A. Khan, and V . Abolghasemi, “Locally optimized adaptive directional time–frequency distributions,”Circuits, Systems, and Signal Processing, vol. 37, no. 8, pp. 3154–3174, 2018

    2018

  16. [17]

    Recovering realistic texture in image super-resolution by deep spatial feature transform,

    X. Wang, K. Yu, C. Dong, and C. C. Loy, “Recovering realistic texture in image super-resolution by deep spatial feature transform,” inProc. IEEE/CVF Conf. Comput. Vis. Pattern Recognit. (CVPR), Salt Lake City, UT, USA, 2018, pp. 606– 615

    2018

  17. [18]

    Adam: A method for stochastic optimization,

    D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” inProc. 3rd Int. Conf. Learn. Represent. (ICLR), San Diego, CA, USA, May 7–9, 2015

    2015

  18. [19]

    Multiscale vessel enhancement filtering,

    A. F. Frangi, W. J. Niessen, K. L. Vincken, and M. A. Viergever, “Multiscale vessel enhancement filtering,” inMedical Image Computing and Computer-Assisted Intervention—MICCAI’98, W. M. Wells, A. Colchester, and S. Delp, Eds. Berlin, Heidelberg: Springer, 1998, pp. 130–137

    1998

  19. [20]

    A robust high-resolution time–frequency representation based on the local optimization of the short-time fractional Fourier transform,

    M. A. Awal, S. Ouelha, S. Dong, and B. Boashash, “A robust high-resolution time–frequency representation based on the local optimization of the short-time fractional Fourier transform,”Digital Signal Processing, vol. 70, pp. 125–144, 2017

    2017

  20. [21]

    Calculation of a constant Q spectral transform,

    J. C. Brown, “Calculation of a constant Q spectral transform,”The Journal of the Acoustical Society of America, vol. 89, no. 1, pp. 425–434, 1991

    1991

  21. [22]

    Fundamental Frequency Estimation in Speech Signals With Variable Rate Particle Filters,

    G. Zhang and S. Godsill, “Fundamental Frequency Estimation in Speech Signals With Variable Rate Particle Filters,”IEEE/ACM Trans. Audio, Speech, Lang. Process., vol. 24, no. 5, pp. 890–900, 2016

    2016

  22. [23]

    A Novel Tempogram Generating Algorithm Based on Matching Pursuit,

    W. Gui, Y . Sun, Y . Tao, Y . Li, L. Meng, and J. Zhang, “A Novel Tempogram Generating Algorithm Based on Matching Pursuit,”Applied Sciences, vol. 8, no. 4, Art. no. 561, 2018

    2018

  23. [24]

    Crossterm-free time-frequency representation exploiting deep convolutional neural network,

    S. Zhang, M. S. R. Pavel, and Y . D. Zhang, “Crossterm-free time-frequency representation exploiting deep convolutional neural network,”Signal Processing, vol. 192, Art. no. 108372, 2022

    2022

  24. [25]

    WVDNet: Time-Frequency Analysis via Semi-Supervised Learning,

    N. Liu, J. Wang, Y . Yang, Z. Li, and J. Gao, “WVDNet: Time-Frequency Analysis via Semi-Supervised Learning,”IEEE Signal Processing Letters, vol. 30, pp. 55– 59, 2023

    2023

  25. [26]

    Robust Time-Frequency Reconstruction by Learning Structured Sparsity,

    L. Jiang, H. Zhang, and L. Yu, “Robust Time-Frequency Reconstruction by Learning Structured Sparsity,”arXiv preprintarXiv:2004.14820, 2020

    arXiv 2004

  26. [27]

    A Data-Driven High-Resolution Time- Frequency Distribution,

    L. Jiang, H. Zhang, L. Yu, and G. Hua, “A Data-Driven High-Resolution Time- Frequency Distribution,”IEEE Signal Processing Letters, vol. 29, pp. 1512–1516, 2022

    2022

  27. [28]

    WVD-GAN: A Wigner-Ville distribution enhancement method based on generative adversarial network,

    D. Quan, F. Ren, X. Wang, M. Xing, N. Jin, and D. Zhang, “WVD-GAN: A Wigner-Ville distribution enhancement method based on generative adversarial network,”IET Radar , Sonar & Navigation, vol. 18, no. 6, pp. 849–865, 2024

    2024

  28. [29]

    TFA-Net: A Deep Learning- Based Time-Frequency Analysis Tool,

    P. Pan, Y . Zhang, Z. Deng, S. Fan, and X. Huang, “TFA-Net: A Deep Learning- Based Time-Frequency Analysis Tool,”IEEE Transactions on Neural Networks and Learning Systems, vol. 34, no. 11, pp. 9274–9286, 2023

    2023

  29. [30]

    Adaptive multi-scale TF-net for high-resolution time-frequency representations,

    T. Chen, Q. Chen, Q. Zheng, Z. Li, Z. Zhang, L. Xie, and H. Su, “Adaptive multi-scale TF-net for high-resolution time-frequency representations,”Signal Processing, vol. 214, Art. no. 109247, 2024

    2024

  30. [31]

    QTFN: A General End-to-End Time- Frequency Network to Reveal the Time-Varying Signatures of the Time Series,

    T. Chen, Y . Jiao, L. Xie, and H. Su, “QTFN: A General End-to-End Time- Frequency Network to Reveal the Time-Varying Signatures of the Time Series,” Big Data Mining and Analytics, vol. 7, no. 3, pp. 905–919, 2024

    2024

  31. [32]

    SparseTFNet: A Physically Informed Autoencoder for Sparse Time-Frequency Analysis of Seismic Data,

    Y . Yang, Y . Lei, N. Liu, Z. Wang, J. Gao, and J. Ding, “SparseTFNet: A Physically Informed Autoencoder for Sparse Time-Frequency Analysis of Seismic Data,” 13 IEEE Transactions on Geoscience and Remote Sensing, vol. 60, Art. no. 4512812, 2022

    2022

  32. [33]

    An automatic fast optimization of quadratic time–frequency distribution using the hybrid genetic algorithm,

    M. A. Awal and B. Boashash, “An automatic fast optimization of quadratic time–frequency distribution using the hybrid genetic algorithm,”Signal Processing, vol. 131, pp. 134–142, 2017

    2017

  33. [34]

    Reduced-interference time–frequency representations and sparse reconstruction of undersampled data,

    Y . D. Zhang, M. G. Amin, and B. Himed, “Reduced-interference time–frequency representations and sparse reconstruction of undersampled data,” inProc. 21st European Signal Processing Conf. (EUSIPCO), Marrakech, Morocco, 2013, pp. 1–5

    2013

  34. [35]

    Genc ¸ay, F

    R. Genc ¸ay, F. Selc ¸uk, and B. Whitcher,An Introduction to Wavelets and Other Filtering Methods in Finance and Economics. San Diego, CA, USA: Academic Press, 2001

    2001

  35. [36]

    A guide to wavelets for economists,

    P. M. Crowley, “A guide to wavelets for economists,”Journal of Economic Surveys, vol. 21, no. 2, pp. 207–267, 2007

    2007

  36. [37]

    Improving the readability of time–frequency and time–scale representations by the reassignment method,

    F. Auger and P. Flandrin, “Improving the readability of time–frequency and time–scale representations by the reassignment method,”IEEE Transactions on Signal Processing, vol. 43, no. 5, pp. 1068–1089, 1995

    1995

  37. [38]

    Wigner distribution function: Relation to short-term spectral estimation, smoothing, and performance in noise,

    A. H. Nuttall, “Wigner distribution function: Relation to short-term spectral estimation, smoothing, and performance in noise,” Naval Underwater Systems Center, New London, CT, USA, Tech. Rep. 8225, Feb. 1988

    1988

  38. [39]

    Deconvolution for positive time–frequency distributions,

    J. W. Pitton, L. E. Atlas, and P. J. Loughlin, “Deconvolution for positive time–frequency distributions,” inProc. 27th Asilomar Conf. Signals, Systems and Computers, Pacific Grove, CA, USA, 1993, vol. 2, pp. 1450–1454

    1993

  39. [40]

    The synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications,

    G. Thakur, E. Brevdo, N. S. Fu ˇckar, and H.-T. Wu, “The synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications,”Signal Processing, vol. 93, no. 5, pp. 1079–1094, 2013

    2013

  40. [41]

    Time–frequency reassignment: From principles to algorithms,

    P. Flandrin, F. Auger, and E. Chassande-Mottin, “Time–frequency reassignment: From principles to algorithms,” inApplications in Time-Frequency Signal Process- ing, A. Papandreou-Suppappola, Ed. Boca Raton, FL, USA: CRC Press, 2003, pp. 179–204

    2003

  41. [42]

    The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,

    N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C.-C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,”Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 454, no. 1971, pp. 903–995, 1998

    1971

  42. [43]

    Variational mode decomposition,

    K. Dragomiretskiy and D. Zosso, “Variational mode decomposition,”IEEE Trans- actions on Signal Processing, vol. 62, no. 3, pp. 531–544, 2014

    2014

  43. [44]

    Design of an optimal piece-wise spline Wigner–Ville distribution for TFD performance evaluation and comparison,

    M. Al-Sa’d, B. Boashash, and M. Gabbouj, “Design of an optimal piece-wise spline Wigner–Ville distribution for TFD performance evaluation and comparison,”IEEE Transactions on Signal Processing, vol. 69, pp. 3963–3976, 2021

    2021

  44. [45]

    The Hilbert Transform,

    F. R. Kschischang, “The Hilbert Transform,” Dept. Elect. & Comput. Eng., Univ. of Toronto, Toronto, ON, Canada, 2006. [Online]. Available: https://www.comm. utoronto.ca/∼frank/notes/

    2006

  45. [46]

    An efficient antialiasing technique,

    X. Wu, “An efficient antialiasing technique,”ACM SIGGRAPH Comput. Graph., vol. 25, no. 4, pp. 143–152, 1991

    1991

  46. [47]

    A Tacholess Order Tracking Method Based on Inverse Short Time Fourier Transform and Singular Value De- composition for Bearing Fault Diagnosis,

    L. Xu, S. Chatterton, P. Pennacchi, and C. Liu, “A Tacholess Order Tracking Method Based on Inverse Short Time Fourier Transform and Singular Value De- composition for Bearing Fault Diagnosis,”Sensors, vol. 20, no. 23, Art. no. 6924, 2020

    2020

  47. [48]

    Eliminating har- monic noise in vibroseis data through sparsity-promoted waveform modeling,

    D. Liu, X. Li, W. Wang, X. Wang, Z. Shi, and W. Chen, “Eliminating har- monic noise in vibroseis data through sparsity-promoted waveform modeling,” Geophysics, vol. 87, no. 3, pp. V183–V191, 2022

    2022

  48. [49]

    Reassigned time–frequency representations of discrete time signals and application to the Constant-Q Transform,

    S. Fenet, R. Badeau, and G. Richard, “Reassigned time–frequency representations of discrete time signals and application to the Constant-Q Transform,”Signal Process., vol. 132, pp. 170–176, Mar. 2017, doi: 10.1016/j.sigpro.2016.10.008

    work page doi:10.1016/j.sigpro.2016.10.008 2017

  49. [50]

    Reassignment and synchrosqueez- ing for general time–frequency filter banks, subsampling and processing,

    N. Holighaus, Z. Pr ˚uˇsa, and P. L. Søndergaard, “Reassignment and synchrosqueez- ing for general time–frequency filter banks, subsampling and processing,”Signal Process., vol. 125, pp. 1–8, Aug. 2016, doi: 10.1016/j.sigpro.2016.01.007

    work page doi:10.1016/j.sigpro.2016.01.007 2016

  50. [51]

    Dynamic Time Signature Recognition, Tempo Inference, and Beat Tracking Through the Metrogram Transform,

    J. M. Cozens and S. J. Godsill, “Dynamic Time Signature Recognition, Tempo Inference, and Beat Tracking Through the Metrogram Transform,” IEEE Open Journal of Signal Processing, vol. 5, pp. 140–149, 2024, doi: 10.1109/OJSP.2023.3344048

    work page doi:10.1109/ojsp.2023.3344048 2024

  51. [52]

    Speech/music classification using features from spectral peaks,

    M. Bhattacharjee, S. R. M. Prasanna, and P. Guha, “Speech/music classification using features from spectral peaks,”IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 28, pp. 1549–1559, 2020

    2020

  52. [53]

    An exhaustive review of automatic music transcription techniques: Survey of music transcription techniques,

    B. S. Gowrishankar and N. U. Bhajantri, “An exhaustive review of automatic music transcription techniques: Survey of music transcription techniques,” in Proc. Int. Conf. Signal Processing, Communication, Power and Embedded System (SCOPES), Paralakhemundi, India, 2016, pp. 140–152

    2016

  53. [54]

    Music deep learning: Deep learning methods for music signal processing—A review of the state of the art,

    L. Moysis, et al., “Music deep learning: Deep learning methods for music signal processing—A review of the state of the art,”IEEE Access, vol. 11, pp. 17031– 17052, 2023

    2023

  54. [55]

    On the quantum correction for thermodynamic equilibrium,

    E. P. Wigner, “On the quantum correction for thermodynamic equilibrium,” Physical Review, vol. 40, no. 5, pp. 749–759, 1932

    1932

  55. [56]

    Matching pursuits with time–frequency dictionaries,

    S. Mallat and Z. Zhang, “Matching pursuits with time–frequency dictionaries,” IEEE Transactions on Signal Processing, vol. 41, no. 12, pp. 3397–3415, 1993

    1993

  56. [57]

    YIN, a fundamental frequency estimator for speech and music,

    A. de Cheveign ´e and H. Kawahara, “YIN, a fundamental frequency estimator for speech and music,”J. Acoust. Soc. Am., vol. 111, no. 4, pp. 1917–1930, Apr. 2002

    1917

  57. [58]

    Th ´eorie et applications de la notion de signal analytique,

    J. Ville, “Th ´eorie et applications de la notion de signal analytique,”C ˆables et Transmissions, vol. 2A, no. 1, pp. 61–74, 1948

    1948

  58. [59]

    Mallat,A Wavelet Tour of Signal Processing: The Sparse Way, 3rd ed

    S. Mallat,A Wavelet Tour of Signal Processing: The Sparse Way, 3rd ed. Amsterdam, The Netherlands: Elsevier/Academic Press, 2009

    2009

  59. [60]

    Flandrin,Time-Frequency/Time-Scale Analysis

    P. Flandrin,Time-Frequency/Time-Scale Analysis. San Diego, CA, USA: Academic Press, 1999

    1999

  60. [61]

    Time–frequency distributions—A review,

    L. Cohen, “Time–frequency distributions—A review,”Proceedings of the IEEE, vol. 77, no. 7, pp. 941–981, 1989

    1989

  61. [62]

    Estimating and interpreting the instantaneous frequency of a signal—Part 1: Fundamentals,

    B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal—Part 1: Fundamentals,”Proceedings of the IEEE, vol. 80, no. 4, pp. 520– 538, 1992

    1992

  62. [63]

    Polynomial Wigner–Ville distributions and their relationship to time-varying higher order spectra,

    B. Boashash and P. O’Shea, “Polynomial Wigner–Ville distributions and their relationship to time-varying higher order spectra,”IEEE Transactions on Signal Processing, vol. 42, no. 1, pp. 216–220, 1994

    1994

  63. [64]

    The interference structure of the Wigner distribution and related time–frequency signal representations,

    F. Hlawatsch and P. Flandrin, “The interference structure of the Wigner distribution and related time–frequency signal representations,” inThe Wigner Distribu- tion—Theory and Applications in Signal Processing, W. Mecklenbr ¨auker and F. Hlawatsch, Eds. Amsterdam, The Netherlands: Elsevier, 1997, pp. 59–133

    1997

  64. [65]

    Improved time–frequency representation of multi- component signals using exponential kernels,

    J. Choi and W. J. Williams, “Improved time–frequency representation of multi- component signals using exponential kernels,”IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 37, no. 6, pp. 862–871, 1989

    1989

  65. [66]

    Time–frequency super-resolution with superlets,

    V . V . Moca, H. B ˆarzan, A. Nagy-D ˆabˆacan, and R. C. Mures ¸an, “Time–frequency super-resolution with superlets,”Nature Communications, vol. 12, Art. no. 337, 2021

    2021

  66. [67]

    A super-resolution spectrogram using coupled PLCA,

    J. Nam, G. J. Mysore, J. Ganseman, K. Lee, and J. S. Abel, “A super-resolution spectrogram using coupled PLCA,” inProc. Interspeech, Makuhari, Japan, 2010, pp. 1696–1699

    2010

  67. [68]

    Attention guided U- Net for accurate iris segmentation,

    S. Lian, Z. Luo, Z. Zhong, X. Lin, S. Su, and S. Li, “Attention guided U- Net for accurate iris segmentation,”Journal of Visual Communication and Image Representation, vol. 56, pp. 296–304, 2018

    2018

  68. [69]

    A method for time–frequency analysis,

    L. Stankovi ´c, “A method for time–frequency analysis,”IEEE Transactions on Signal Processing, vol. 42, no. 1, pp. 225–229, 1994

    1994

  69. [70]

    Synchroextracting transform,

    G. Yu, M. Yu, and C. Xu, “Synchroextracting transform,”IEEE Trans. Ind. Electron., vol. 64, no. 10, pp. 8042–8054, 2017

    2017

  70. [71]

    On a measure of divergence between two statistical populations defined by their probability distributions,

    A. Bhattacharyya, “On a measure of divergence between two statistical populations defined by their probability distributions,”Bull. Calcutta Math. Soc., vol. 35, pp. 99–109, 1943

    1943

  71. [72]

    Divergence measures based on the Shannon entropy,

    J. Lin, “Divergence measures based on the Shannon entropy,”IEEE Trans. Inf. Theory, vol. 37, no. 1, pp. 145–151, Jan. 1991

    1991

  72. [73]

    Prolate spheroidal wave functions, Fourier analysis and uncertainty—I,

    D. Slepian and H. O. Pollak, “Prolate spheroidal wave functions, Fourier analysis and uncertainty—I,”Bell Syst. Tech. J., vol. 40, no. 1, pp. 43–63, 1961

    1961

  73. [74]

    A measure of some time–frequency distributions concentration,

    L. Stankovi ´c, “A measure of some time–frequency distributions concentration,” Signal Processing, vol. 81, no. 3, pp. 621–631, 2001

    2001

  74. [75]

    The Hungarian method for the assignment problem,

    H. W. Kuhn, “The Hungarian method for the assignment problem,”Naval Research Logistics Quarterly, vol. 2, nos. 1–2, pp. 83–97, 1955

    1955

  75. [76]

    de Boor,A Practical Guide to Splines

    C. de Boor,A Practical Guide to Splines. New York, NY , USA: Springer-Verlag, 1978. [76]IEEE Recommended Practice for Speech Quality Measurements, IEEE Std. 297- 1969, May 1969, doi: 10.1109/IEEESTD.1969.7405210. VI. BIOGRAPHY James M. Cozens(Member, IEEE) is a Ph.D. candidate in the Probabilistic Systems, Information, and Inference Group (ψ 2) at the Uni...

    work page doi:10.1109/ieeestd.1969.7405210 1978