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Optimal Window and Lattice in Gabor Transform. Application to Audio Analysis.

Helene Lachambre1, Benjamin Ricaud2, Guillaume Stempfel1

  • 1Genesis Acoustics, Domaine du Petit Arbois, 13545 Aix-en-Provence, France.

Proceedings. International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
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Summary
This summary is machine-generated.

This study introduces optimal lattice and window adaptation for Discrete Gabor Transform, enhancing time-frequency analysis of non-stationary signals. Improved performance is shown in distinguishing close frequencies and estimating frequency and SNR.

Keywords:
Audio signal processingChirped Gaussian windowDiscrete Gabor TransformOptimal latticeOptimal window

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Area of Science:

  • Signal Processing
  • Time-Frequency Analysis
  • Applied Mathematics

Background:

  • Discrete Gabor Transform (DGT) is crucial for time-frequency analysis.
  • Existing methods may lack optimal parameters for non-stationary signals.
  • Generalized Gaussian windows offer flexibility but require adaptation.

Purpose of the Study:

  • To introduce optimal lattice and window adaptation for DGT.
  • To improve time-frequency analysis for non-stationary signals.
  • To demonstrate enhanced performance in specific signal analysis tasks.

Main Methods:

  • Utilizing optimal lattice and optimal window selection in DGT computation.
  • Implementing a local window adaptation technique for generalized Gaussian windows.
  • Applying the methods to three distinct time-frequency analysis problems.

Main Results:

  • Demonstrated improvements in distinguishing closely spaced frequencies.
  • Showcased enhanced accuracy in frequency estimation.
  • Achieved better Signal-to-Noise Ratio (SNR) estimation.
  • Validated results using real-world audio signals.

Conclusions:

  • Optimal lattice and window adaptation significantly improve DGT performance.
  • The proposed local window adaptation is effective for non-stationary signals.
  • The enhanced DGT provides superior results for critical time-frequency analysis tasks.