Generalized Morse Wavelets as a Superfamily of Analytic Wavelets

Details Generalized Morse Wavelets as a Superfamily of Analytic Wavelets Generalized Morse Wavelets as a Superfamily of Analytic Wavelets

2012-03-15

arxiv.org/abs/1203.3380v1

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Scientific paper

The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets. Details of the time/frequency concentration, frequency-domain symmetry, and Gaussianity of these wavelets are investigated. The generalized Morse wavelets are controlled by two parameters, one determining the Fourier-domain bandwidth, and the second, called $\gamma$, determining the lowest-order departure of the wavelet from a Gaussian form. For integer values of $\gamma$, the most symmetric, most nearly Gaussian, and generally most time-frequency concentrated member of this wavelet family occurs for $\gamma=3$. The special properties of these "Airy wavelets"-so called because they derive from an inhomogeneous Airy function-make them an ideal analytic wavelet family for general purpose use. This provides a simple rational as to how to choose an appropriate analytic wavelet.

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