Generalized Morse Wavelets as a Superfamily of Analytic Wavelets

Abstract

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 {\em shape} with fixed bandwidth may be modified by varying a second parameter, called $\gamma$. For integer values of $\gamma$, the most symmetric, most nearly Gaussian, and generally most time-frequency concentrated member of the superfamily is found to occur for $\gamma =3$. 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.

Cited by in corpus (16)

• Element analysis: a wavelet-based method for analyzing time-localized events in noisy time series
• Characterization of Analytic Wavelet Transforms and a New Phaseless Reconstruction Algorithm
• Electronic Quantum Coherence in Glycine Molecules Probed with Ultrashort X-ray Pulses in Real Time
• Magnetopause ripples going against the flow form azimuthally stationary surface waves
• The Generalized Fourier Transform: A Unified Framework for the Fourier, Laplace, Mellin and $Z$ Transforms
• On the estimation of the evolutionary power spectral density
• Soft-Output Signal Detection for Cetacean Vocalizations Using Spectral Entropy, K-Means Clustering and the Continuous Wavelet Transform
• Studies on Generalized Fourier Representations and Phase Transforms
• Linear and synchrosqueezed time-frequency representations revisited. Part I: Overview, standards of use, related issues and algorithms
• Periodic recurrent waves of Covid-19 epidemics and vaccination campaign
• Bilinear noise subtraction at the GEO 600 observatory
• Dispersive coherent Brillouin scattering spectroscopy
• PENELLOPE V. The magnetospheric structure and the accretion variability of the classical T Tauri star HM Lup
• On the external forcing of global eruptive activity in the past 300 years
• Classifying herbal medicine origins by temporal and spectral data mining of electronic nose
• Vortex-Induced Drag Forecast for Cylinder in Non-uniform Inflow