Scaling the result of MW convolution

Is it possible to scale the result of Morlet wavelet wavelet convolution so that amplitude values are in the same unit as the original signal?

Thanks very much,

Hi Emily. I talk about normalizing wavelets in a few places, including my Udemy course, possibly YT videos, perhaps this paper (and accompanying code), and perhaps some other places.

The short version is that you max-value normalize the wavelet in the frequency domain (something like cmwX = cmwX/max(abs(cmwX)), where cmwX is the FFT of the complex Morlet wavelet, and then I think you need to multiply by 2 to account for the empty negative spectrum. I forget that detail off-hand. But running a simulation with a known signal will tell you if you’re doing the right thing.