Variable-windowed spectrograms: connecting Cohen's class and the wavelet transform

Abstract

Defines a class of time-frequency representations called variable-windowed spectrograms (VWS), and explores the link between the two independently developed categories of time-frequency representations: Cohen's class and the wavelet transform (WT). By expanding upon the conventional (fixed-windowed) spectrogram, the VWS provides flexible time-frequency localizations depending on the selection of the variable (i.e., time- and frequency-dependent) windows. It is shown that the VWS is a subclass of Cohen's class and that a particular constraint on the window of the VWS produces a distribution which is equivalent to the modulus squared of a WT. Some aspects of the VWS are discussed in the ambiguity, temporal correlation, spectral correlation, and time-frequency domains.<>