基于小波的广义时频分布及其与Cohen类的关系

The Generalized Time-Frequency Distribution Based on Wavelet and Its Relation with Cohen's Class

STFT，WT，WVD和Cohen类是目前信号分析和处理的有力工具。本文用WT的二次型时频形式分析了线性时频特性，研究了尺度图和变化窗谱图与Cohen类之间的关系；将尺度图纳入到Cohen类的框架，从而使WT广义化为时频域、时延频偏域的双线性时频分布以及谱相关域的二维频率分布；定义了尺度图、小波模糊函数(WAF)和小波谱相关函数(WSCF)；分析了它们的物理意义。推导并仿真了单频、双频和高斯白噪声的WSCF，分析了各自的特性。最后通过引入一种离散小波变换的加密算法，解决了小波时频分布的计算问题。

STFT, WT, WVD and Cohen＇s class are the useful tools of signal processing. This paper analyzes the bilinear TF based on WT, and the relation between the scalogram, VWS and Cohen＇s class, Furthermore, the scalogram is classified into Cohen＇s class, and then WT is generalized to TF domain（scalogram）, ambiguity domain（wavelet AF） and frequency/frequency delay domain（WSCF）. The WSCF characteristics of mono-frequency, dual-frequency, WGN, and fractal stochastic noise are analyzed. Finally, a dense algorithm of discrete WT is introduced to the computation of generalized TF distribution based on WT.