Comparing global wavelet spectrum to Fourier spectrum

I have used "cwtft" to get the wavelet coefficients using 'morl'. When I sqaure the coefficients and average them along time, and them compare them to the Fourier power spectrum, I see that the curve differ by a multiplicative factor. I came across a forum which said that multipliying the wavelet coefficients by "sqrt(2*dt)", where dt=sampling interval, would help. Using this, I get the required match between the two spectra. I would like to know how this constant comes about.

[Gisela Clemente]

Hello! Can you give me the code? I need to do something like that but I dont know how. Thanks!

Answer 1

[Sai Sri Pathuri]

Following are the equations of continuous wavelet transform and discrete Fourier transform which may help you in understanding about the multiplicative factor

where N-Number of samples, a – scale, b - time position, Δt = 1/fs - sampling period