Higher-order properties of analytic wavelets
IEEE Transactions on Signal Processing
The monogenic wavelet transform
IEEE Transactions on Signal Processing
Bivariate instantaneous frequency and bandwidth
IEEE Transactions on Signal Processing
A statistical analysis of morse wavelet coherence
IEEE Transactions on Signal Processing
Wavelet ridge estimation of jointly modulated multivariate oscillations
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
On the analytic wavelet transform
IEEE Transactions on Information Theory
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This paper examines the 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 (β, γ); we extend results derived for the special case β = γ = 1 and include a proof of "the resolution of identity." The wavelets are easy to compute using the discrete Fourier transform (DFT) and, for (β, γ) = (2m, 2), can be computed exactly. A correction of a previously published eigenvalue formula is given. This shows that for γ 1, generalized Morse wavelets can outperform the Hermites in energy concentration, contrary to a conclusion based on the γ = 1 case. For complex signals, scalogram analyses must be carried out using both the analytic and anti-analytic complex wavelets or odd and even real wavelets, whereas for real signals, the analytic complex wavelet is sufficient.