Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Disentangling Modes and Interference in the Spectrogram of Multicomponent Signals

Kévin Polisano, Sylvain Meignen, Nils Laurent, Hubert Leterme

TL;DR

This work tackles interference in the spectrograms of multicomponent signals, which hampers ridge detection and instantaneous frequency estimation. It develops two complementary approaches: a variational cartoon-texture decomposition based on total variation and a G-norm texture space with alternate projections, and a supervised U-Net trained on synthetic data to separately recover the mode and interference terms. The authors demonstrate that both methods can extract the interference while preserving mode structure, and they introduce an adaptive windowing strategy that selects window lengths locally to minimize interference in the time-frequency representation, thereby enhancing ridge detection. The proposed framework improves time-frequency analysis under strong interference and provides practical avenues for more robust frequency estimation in complex signals. The methods are validated on synthetic data, with discussions on generalization and potential extensions such as explicit noise modeling and Plug-and-Play integrations.

Abstract

In this paper, we investigate how the spectrogram of multicomponent signals can be decomposed into a mode part and an interference part. We explore two approaches: (i) a variational method inspired by texture-geometry decomposition in image processing, and (ii) a supervised learning approach using a U-Net architecture, trained on a dataset encompassing diverse interference patterns and noise conditions. Once the interference component is identified, we explain how it enables us to define a criterion to locally adapt the window length used in the definition of the spectrogram, for the sake of improving ridge detection in the presence of close modes. Numerical experiments illustrate the advantages and limitations of both approaches for spectrogram decomposition, highlighting their potential for enhancing time-frequency analysis in the presence of strong interference.

Disentangling Modes and Interference in the Spectrogram of Multicomponent Signals

TL;DR

This work tackles interference in the spectrograms of multicomponent signals, which hampers ridge detection and instantaneous frequency estimation. It develops two complementary approaches: a variational cartoon-texture decomposition based on total variation and a G-norm texture space with alternate projections, and a supervised U-Net trained on synthetic data to separately recover the mode and interference terms. The authors demonstrate that both methods can extract the interference while preserving mode structure, and they introduce an adaptive windowing strategy that selects window lengths locally to minimize interference in the time-frequency representation, thereby enhancing ridge detection. The proposed framework improves time-frequency analysis under strong interference and provides practical avenues for more robust frequency estimation in complex signals. The methods are validated on synthetic data, with discussions on generalization and potential extensions such as explicit noise modeling and Plug-and-Play integrations.

Abstract

In this paper, we investigate how the spectrogram of multicomponent signals can be decomposed into a mode part and an interference part. We explore two approaches: (i) a variational method inspired by texture-geometry decomposition in image processing, and (ii) a supervised learning approach using a U-Net architecture, trained on a dataset encompassing diverse interference patterns and noise conditions. Once the interference component is identified, we explain how it enables us to define a criterion to locally adapt the window length used in the definition of the spectrogram, for the sake of improving ridge detection in the presence of close modes. Numerical experiments illustrate the advantages and limitations of both approaches for spectrogram decomposition, highlighting their potential for enhancing time-frequency analysis in the presence of strong interference.

Paper Structure

This paper contains 13 sections, 13 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. First Model Based on a Variational Approach
  3. Oscillating Interference Patterns on Toy Models
  4. TV-minimization using the $G$-norm
  5. Implementation with Alternate Projections
  6. Second Model Based on Deep Learning
  7. A Supervised Approach Based on U-Net
  8. Synthetic Data Generation with IF and IA Splines
  9. Implementation Details
  10. Results and Discussions
  11. Separating Mode parts from Interference Part
  12. Adapting the Window Length Based on Interference Patterns
  13. Conclusion and Perspectives

Figures (4)

  • Figure 1: Spectrogram of two harmonics \ref{['eq:spect']} separated by $\delta f = 40Hz$ (left), along with its decomposition into a "Mode part" (middle) and an "Interference part" (right).
  • Figure 2: Illustration of the U-Net decomposition of the spectrogram \ref{['eq:t1']}-\ref{['eq:t3']}.
  • Figure 3: Spectrograms of a noisy signal consisting of (a) the superposition of a linear and hyperbolic chirps ($w=20$, $\mathrm{SNR}=10$) and (d) of two spline modes, generated by the procedure described in Section \ref{['sec:synthetic']} ($w=23$, $\mathrm{SNR}=10$). (b)-(e) Modes parts and (c)-(f) Interference parts in the spectrogram decomposition, presented in the following order: ground truth, TV-based decomposition, and U-Net predictions.
  • Figure 4: (a) $V_{\mathrm{adap}}$ with detected TF ridges, (b) evolution of the interference-to-signal ratio as a function of window size $w$ at time indices $n=40$ and $n=160$ (resp. $t_n=0.15$ and $t_n=0.62$ on the time axis), with the minimum ratio achieved at $\hat{q}_n$\ref{['eq:opt_q']} highlighted in red.