Generalized Morse Wavelets as a Superfamily of Analytic Wavelets

By Jonathan M. Lilly, Sofia Charlotta Olhede. IEEE Transactions on Signal Processing, 2012

416 citations recorded by the source corpus.

The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets, subsuming eight apparently distinct types of analysis filters into a single common form. This superfamily of analytic wavelets provides a framework for systematically investigating wavelet suitability for various applications. In addition to a parameter controlling the time-domain duration or Fourier-domain bandwidth, the wavelet shape with fixed bandwidth may be modified by varying a second parameter, called γ. For integer values of γ, the most symmetric, most nearly Gaussian, and generally most time-frequency concentrated member of the superfamily is found to occur for γ = 3. These wavelets, known as “Airy wavelets,” capture the essential idea of popular Morlet wavelet, while avoiding its deficiencies. They may be recommended as an ideal starting point for general purpose use.

Subfields: Computer Vision and Pattern Recognition, Economics and Econometrics, Media Technology

View Paper: https://www.semanticscholar.org/paper/805c752f57043800044f539093ec1727b5495907

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Citations in the corpus

• Brain‐to‐brain synchrony in parent‐child dyads and the relationship with emotion regulation revealed by fNIRS‐based hyperscanning (2018, background): “Thus, for this parametrization, the GMW captures the idea of the Morlet wavelet, but shows improved performance for highly time-localized settings (Lilly and Olhede, 2012).”