I have followed a lot of stuff on mike cohens website and have managed to make a filterbank of Morlet wavelets and convolve with an incoming block of samples. This of course is a computationally heave approach so am Now wanting to try this in the frequency domain.
I convert the wavelets to the frequency domain (perform DFT of each one) and have performed DFT on an incoming block of samples (making sure the sample length and kernel length match. I then multiply each FFT sample to give me a result and save it in a matrix, giving me the filtered FFT for each band.
I am now confused as to what this actually is. If I do an inverse DFT I should get back to the time domain, giving me power in time for each filter in the bank, so I could display this in a scalogram. However I would quite like to display the entire filtered spectrum at this point, but am lost on what the results are.
Because each filterbank corresponds to a centre frequency, but then each ‘frequency bin’ in the original DFT signal corresponds to a frequency. How do I interpret this to give me a filtered DFT for the average of the incoming signal? Or would I have to convert back to the time domain for each filterbank and then I can choose an index for each filterbank to get the energy for that point in time?
The full scalogram model is the next part of my journey, but my current aim is to produce a filtered DFT. a DFT on its own lacks the low end detail I need, and too many high frequency points. I know that increasing my sample size will give me frequency resolution but I want to experiment to find an inbetween compromise for my needs.