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:
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.
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
