AN ANALYSIS OF SOME TIME-FREQUENCY AND TIME-SCALE DISTRIBUTIONS

This paper presents an analysis of the representation of instantaneous frequency and group delay using time-frequency transforms or distribu tions of energy density domain. The time-frequency distributions which ideally represent the instantaneous frequency of group delay (ITFD) a re defined. Closeness to the ITFD is chosen as a criterion for compari son of various commonly used distributions. It is shown that the Wigne r distribution is the best among them, with respect to this criterion. The wavelet and scaled forms of the Wigner distribution are defined a nd analyzed. In the second part of the paper we extended the analysis to the multicomponent signals and cross terms effects. On the basis of that analysis, an efficient method, derived from the analysis of the Wigner distribution defined in the frequency domain, is proposed. This method provides some substantial advantages over the Wigner distribut ion. The theory is illustrated on numerical examples.