Generalized Morse Wavelets as a Superfamily of Analytic Wavelets

摘要

The generalized Morse wavelets are shown to constitute a superfamily thatessentially encompasses all other commonly used analytic wavelets, subsumingeight apparently distinct types of analysis filters into a single common form.This superfamily of analytic wavelets provides a framework for systematicallyinvestigating wavelet suitability for various applications. In addition to aparameter controlling the time-domain duration or Fourier-domain bandwidth, thewavelet {\em shape} with fixed bandwidth may be modified by varying a secondparameter, called $\gamma$. For integer values of $\gamma$, the most symmetric,most nearly Gaussian, and generally most time-frequency concentrated member ofthe superfamily is found to occur for $\gamma=3$. These wavelets, known as"Airy wavelets," capture the essential idea of popular Morlet wavelet, whileavoiding its deficiencies. They may be recommended as an ideal starting pointfor general purpose use.