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analytical expression for Morse wavelet

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subbu
subbu on 22 Apr 2021
Edited: Wayne King on 4 May 2021
What's the analytical expression for morse wavelet used in cwt in time domain?

Answers (1)

Wayne King
Wayne King on 4 May 2021
Edited: Wayne King on 4 May 2021
Morse wavelets are defined in the frequency domain, so the analytic expressions for the Morse wavelets involve an integral. Obviously the exact form of this integral depends on your convention for the Fourier transform and its inverse. Using the convention with no in the exponent and in front of the inverse, the expression for the Morse wavelet in time is just:
where is a normalizing constant. You can start with and derive subsequent Morse wavelets for any βas long as γis fixed by differentiating Morse wavelet with respect to time.
So starting with:
We have (inductively):
Hope that helps,
Wayne

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