Investigation of Signal Characteristics Using the Continuous Wavelet Transform

he continuous wavelet transform (CWT) displays the scale-dependent structure of a signal as it varies in time. This scale-dependent structure, in turn, is essentially the instantaneous frequency, so that the CWT provides a view of the frequency versus time behavior of the signal and therefore has great potential as a preliminary tool for investigating wideband, nonstationary, or other types of signals having time-dependent spectral characteristics. In this article, the CWT is considered as a qualitative tool that can be used to analyze such signals. The results of this analysis would then be used to construct appropriate signal processing algorithms to detect, characterize, and classify the signals. A particular complex-valued wavelet, proposed by Morlet, has good properties for use as the kernel in a qualitative CWT. These properties are presented, and the use of the CWT for studying wideband communications signals and for finding features that might be of phenomenological significance in a seismic signal is discussed.