Comparison of measures of time-frequency distribution optimization

Abstract

This article describes the problems of time-frequency representation optimization. The goal is to achieve compromise between good resolution and reduced cross terms. The quantitative measures used for this optimization are described. For the case of a simulated signal a measure based on mean squared error is proposed. The proposed method compares an optimized result to the ideal representation obtained as sum of Wigner-Ville distributions of mono-component signals. Three simulated signals are used to compare optimization of Choi-Williams Distribution, Gabor spectrogram, Short-time Fourier transform and S-method. The optimization is realized on the basis of four quantitative measures: Rényi entropy, Jones-Parks measure, Stanković measure and proposed method. Results show problematic use of Jones-Parks measure for optimization and comparable optimization of all tested time-frequency distributions by means of three usable measures. For practical use with real signal, S-method with Rényi or Stanković measure is recommended.