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Optimising Time-Frequency Distributions: A Surface Metrology Approach.

Damir Malnar1, Miroslav Vrankic1

  • 1Faculty of Engineering, University of Rijeka, Vukovarska 58, 51000 Rijeka, Croatia.

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Summary
This summary is machine-generated.

Optimizing time-frequency signal processing representations is crucial. A new Abbot-Firestone curve-based measure aligns numerical results with visual assessments, improving signal analysis accuracy.

Keywords:
Abbotcurvedistributionevolutionarykernelmetrologymultiformoptimisationsurfacetime-frequency

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Area of Science:

  • Signal Processing
  • Applied Mathematics

Background:

  • Time-frequency signal processing enhances analysis over temporal or frequency-only methods.
  • Current optimization practices rely on visual inspection and measures like Rényi entropies or Stanković's energy concentration.
  • Filter kernel adaptability can create discrepancies between numerical measures and visual quality of time-frequency representations.

Purpose of the Study:

  • To propose a novel performance measure for optimizing time-frequency signal representations.
  • To introduce a parameter-free, minimalistic differential evolution variant for optimization.
  • To address the discrepancy between numerical metrics and visual assessment in adaptive kernel scenarios.

Main Methods:

  • A new performance measure derived from the Abbot-Firestone curve, analogous to surface metrology volume parameters, was developed.
  • A minimalistic, parameter-free differential evolution algorithm with a population of five members was employed.
  • The multiform tiltable exponential kernel was optimized using Rényi entropy, Stanković's energy concentration, and the proposed measure on synthetic and real-life signals.

Main Results:

  • The proposed optimization algorithm demonstrated reliable convergence across all tested measures and signals.
  • The novel Abbot-Firestone curve-derived measure showed consistent alignment between reported numerical values and visual assessments.
  • Optimized time-frequency distributions were evaluated using multiple measures and visual inspection.

Conclusions:

  • The proposed performance measure offers a more reliable objective function for optimizing time-frequency representations.
  • The minimalistic differential evolution variant effectively optimizes kernel parameters.
  • This approach enhances the accuracy and interpretability of time-frequency signal analysis.