Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 60, Issue 11, Pages 6036-6041Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2012.2210890
Keywords
Amplitude modulation; continuous wavelet transform; frequency modulation; Hilbert transform
Categories
Funding
- Physical Oceanography program of the United States National Science Foundation [0849371]
- Engineering and Physical Sciences Research Council of the United Kingdom [EP/I005250/1]
- EPSRC [EP/I005250/1] Funding Source: UKRI
- Directorate For Geosciences
- Division Of Ocean Sciences [0849371] Funding Source: National Science Foundation
- Engineering and Physical Sciences Research Council [EP/I005250/1] Funding Source: researchfish
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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 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.
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