Wow . Just wow. This is such a great explanation.

Hi, Thanks, nice illustrations and examples. Can you make a video about deconvolution of 1D signals? For example, if we have the observed signal and the input kernel, how to identify the system function (reflectivity series). It is really hard to understand this concept because it is an inverse problem.

How to make the signal that you were using to explain morlet wavelet as spectral filter or similar random signal that are combination of different frequencies and are not stationary in matlab?

such an elegant explanation! thanks a lot!

Spectacular

Thank you sir ,keep going and make your powerful and fantastic totourial

Thank you very much for your wonderful illustration. I have a question about IFFT, hoping that you could explain further. As you mentioned the transformation of frequency spectrum back into time-domain using IFFT can result in the same time series pattern. How is the sequence conveyed in the frequency spectrum? Could it be possible that, after IFFT, the frequencies are all there but they are in different order? Thank you.

Thank you Mike for the great video! Im struggling to wrap my head around one thing though.. At this panel that starts at around 11:00 we see the signal, kernel, result of convolution and the image of spectral multiplication. When I go through it from top to bottom, through convolution, it seems perfectly intuitive. We have this signal changing with time, and the convolutions with the wavelet of certain frequency helps us to clearly uncover, let's say, this "blob" of that frequency starting after approx. 2/3 of the orange time series (Result). So, there is some temporal dynamics, and the convolution helps to emphasize it. That's okay. However, I can't get how the inverse fourier transform (when mentally going from 'frequency' timeseries up to 'Result') could recover the same blob at the exact time? I mean, how the frequency spectrum, multiplied by that gaussian image of wavelet in frequency domain - which makes it very localized to short range of frequencies - how this frequency spectrum after it is deciphered back to time domain can still hold the information about that exact timing of that blob on the orange line? Thanks

Thanks for the video! at 17:00, what do you mean by saying "that length is n+m-1"? I think n+m-1 is the length of the convolution result. but for spectra multiplication, I think the frequency resolution matters? although the length of signal (n)/kernel (m) will affect frequency resolution. and I can't understand why IFFT will get a result of length n+m-1? I think n+m-1 is originated from the "time-series sliding with zero-padding" procedure, which is the convolution in time domain, i.e., the top panel of your comparison plot, but 5-steps here are related to the bottom panel, right? I know they are equivalent, but I expect with the procedure done in frequency domain, there is no need for zero-padding (thus no need to cut of "wings") as we did in the time-series sliding procedure? but seems that you also mentioned if the signal and kernel have different lengths, we will zero-padding when we do FFTs for them (separately). the purpose for this is to get the same frequency resolution in order to multiply spectra? I know you emphasized that zero-padding in the time-series sliding vs. FFT are different things, but I get confused... sorry for the long question list

Thankyou

what is the optimal amplitude of the kernel should be? after convolution, my signal's amplitude becomes very high, in my case more than my kernel.

Why do you 0-pad m on boths sides, instead of m/2 on both sides. If you 0 padded only m/2 on both sides, wouldn't this mean you wouldn't require step 5 (cutting off the wings)