Nonnegative Time-Frequency Distributions for Sparse Representation of Dispersion Signal

Abstract

Sparse decomposition decompose signal over a family of elementary functions that are well adapted to the signal's local structures. The signal time-frequency distribution can be obtained by summing the weighted Wigner-Ville distribution of the best-matched elementary functions. This time-frequency distribution has well resolution by suppressing the cross-term among the elementary functions. When the frequencies of the elementary functions are nonlinear, much of cross-terms will undesirably appear in themselves and the final Wigner-Ville distribution. This paper proposes a method for calculating a nonnegative and cross-term free time-frequency distribution based on a special class of semi-affine transformation group. A nongetative cross-term free time-frequency distribution is devised for a special atom dictionary in which the element function has Gaussian-envelop and frequency varies with dispersion low. Theoretical predictions and numerical results indicate that the proposed method can result in the most visually appealing time-frequency distributions for highly nonstationary signals.