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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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Pseudo-Bayesian Approach for Robust Mode Detection and Extraction Based on the STFT.

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  • 1LTCI, Télécom Paris, 91120 Palaiseau, France.

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Summary

This study introduces a novel pseudo-Bayesian algorithm for disentangling mixed signals and their components. The method effectively estimates instantaneous frequencies and reconstructs signals, even with additive noise.

Keywords:
assumed density filteringhypothesis testnonstationary component estimationrobust divergencessynchrosqueezingtime-frequencyvariational approximation

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Area of Science:

  • Signal Processing
  • Data Analysis
  • Mathematical Modeling

Background:

  • Nonstationary signals are complex mixtures of underlying components.
  • Accurate separation of these components is crucial for signal analysis.
  • Existing methods struggle with noise and precise component localization.

Purpose of the Study:

  • To develop a robust algorithm for disentangling multicomponent nonstationary signals.
  • To accurately estimate the instantaneous frequency of individual signal modes.
  • To enhance signal reconstruction quality in the presence of additive noise.

Main Methods:

  • A novel pseudo-Bayesian algorithm for instantaneous frequency estimation.
  • A detection algorithm to define component time-frequency regions.
  • A new reconstruction approach using nonbinary band-pass synthesis filters.

Main Results:

  • Successful disentanglement of nonoverlapping multicomponent signals.
  • Accurate estimation of instantaneous frequencies for signal modes.
  • Enhanced signal reconstruction quality compared to state-of-the-art methods.

Conclusions:

  • The proposed pseudo-Bayesian approach offers effective signal disentanglement.
  • The method demonstrates robustness against additive noise.
  • Validated through experiments with synthetic and real-world data.