Abstract
This paper examines class of generalized Morse wavelets, which are eigenfunction wavelets suitable for use in time-varying spectrum estimation via averaging of time-scale eigenscalograms. Generalized Morse wavelets of order k (the corresponding eigenvalue order) depend on a doublet of parameters (/spl beta/, /spl gamma/); we extend results derived for special case /spl beta/ = /spl gamma/ = 1 and include a proof of the resolution of identity. The wavelets are easy to compute using discrete Fourier transform (DFT) and, for (/spl beta/, /spl gamma/) = (2m, 2), can be computed exactly. A correction of a previously published eigenvalue formula is given. This shows that for /spl gamma/ > 1, generalized Morse wavelets can outperform Hermites in energy concentration, contrary to a conclusion based on /spl gamma/ = 1 case. For complex signals, scalogram analyses must be carried out using both analytic and anti-analytic complex wavelets or odd and even real wavelets, whereas for real signals, analytic complex wavelet is sufficient.
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