The wide sense time-frequency representation based on the wavelet and its relation with Cohen´s class

This paper analyzes the bilinear TFR based on the WT, and the relation between the scalograms, VWS and Cohen´s class. Furthermore, the scalograms are classified into the Cohen´s class, and then the WT is generalized to TF domain (scalograms), ambiguity domain (wavelet AF) and frequency/frequency delay domain (wavelet SCF). The WSCF´s characteristics of mono-frequency, dual-frequency, WGN, and fractal stochastic noise are analyzed. The research shows that the WSCF have the similar characteristics with the SCF in many aspects, but especially for fractal noise, the WSCF have high quality of interference-rejection, which is advantageous for signal processing at the presence of fractal noise. Finally, a dense algorithm of discrete of WT is introduced to the computation of WS TFR based on the WT.