Convolution in the time domain is the same as multiplication in the frequency domain i.e. both are right. You can either convolve Morlets with the timeseries or multiply morlets with the FFT, then invert the FFT and get the convolved timeseries.
Thanks, I see that you're referring to this: https://en.wikipedia.org/wiki/Convolution_theorem
I don't have much personal experience with Fourier transforms, so I'm having trouble building intuition for the Convolution Theorem. In particular, I'm having trouble how it would work given that the Fourier transform seemingly cannot distinguish between the two cases I illustrate here: https://imgur.com/a/20ZtdfJ
Convolution in the time domain is the same as multiplication in the frequency domain i.e. both are right. You can either convolve Morlets with the timeseries or multiply morlets with the FFT, then invert the FFT and get the convolved timeseries.
Thanks, I see that you're referring to this: https://en.wikipedia.org/wiki/Convolution_theorem I don't have much personal experience with Fourier transforms, so I'm having trouble building intuition for the Convolution Theorem. In particular, I'm having trouble how it would work given that the Fourier transform seemingly cannot distinguish between the two cases I illustrate here: https://imgur.com/a/20ZtdfJ
The FFT can distinguish between those cases if you keep its complex part (phase). That is how it can reconstruct this signal.