MATLAB's implementation of cwt uses the complex morlet wavelet as:

psi(x) = (pi*Fb)^(-0.5)*exp(2*1j*pi*Fc*x)*exp(-(x^2)/Fb);

However, it is possible to implement the cwt in the Fourier domain (cwtft). In this case, MATLAB uses a slightly different version of the Morlet wavelet:

psi = (pi^(1/4)).*exp(2*pi*1j*t)*exp(-(t.^2)/2);

The question is: how can I change (or insert) the frequency band parameter in the cwtft version?

Would be something like:

psi2 = (Fb*pi.^(1/4)).*exp(2*pi*Fc*1j*t).*exp(-(t.^2)/(Fb*2));

if yes, how is the Fourier version of psi2 (because the implementation takes the fourier transform of psi2)?


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