Generalized Morse wavelets
By Sofia Charlotta Olhede, Andrew T. Walden. IEEE Transactions on Signal Processing, 2002
301 citations recorded by the source corpus.
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 (/spl beta/, /spl gamma/); we extend results derived for the special case /spl beta/ = /spl gamma/ = 1 and include a proof of "the resolution of identity." The wavelets are easy to compute using the 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 the Hermites in energy concentration, contrary to a conclusion based on the /spl gamma/ = 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.
Subfields: Computer Vision and Pattern Recognition, Control and Systems Engineering, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/4a847bcd05bc22e2271b6ff695fbe5540755b56d
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Citations in the corpus
- The continuous wavelet transform : a primer (2011, unknown): “The results of this section are derived from the papers by Olhede and Walden [34] and Lilly and Olhede [30, 31].”
- THE CONTINUOUS WAVELET TRANSFORM: MOVING BEYOND UNI‐ AND BIVARIATE ANALYSIS (2014, unknown): “The results of this section are derived from the papers by Olhede and Walden ( 2002 ) The Morlet wavelets are a one - parameter family of functions , …rst introduced in Goupillaud , Gross - man and Morlet ( 1984 ) , and given by !”
- Spatiospectral Concentration on a Sphere (2004, unknown): “Time-frequency and time-scale concentration in more general settings and a variety of geometries has subsequently been studied by several authors, e.g., [7, 11, 13, 14, 16, 17, 18, 21, 37, 40, 43, 44, 51].”
- Generalized Morse Wavelets as a Superfamily of Analytic Wavelets (2012, background): “A desirable characteristic for a wavelet would be to combine the special properties of a Gaussian—which is in a sense the most time/frequency concentrated function—with the constraints necessary for an analytic wavelet.”