# Wavelet signal analysis approach for multi-mode, noisy signal

I have a signal that I am trying to analyze via Matlab's CWT functions. The signal has two distinct oscillating components and I would like to extract the decay factor from each of them. Here is what the raw time-domain data looks like:

and the CWT using Morse wavelet (which gave me the best frequency resolution):

I then used other software (Igor Pro with plug-ins) to take cuts of the two prominent frequency ridges (Below, time is on the x axis). For the high-frequency one, I was able to fit to a decaying exponential:

which looks fine and dandy to me. But doing the same procedure on the low frequency ridge, it looks like this: .

My question is: since the HF data fits well to an exponential, and I've tested this same procedure with known frequencies and decay rates, why does the low-frequency CWT amplitude v. time look the way that it does? Given the raw data, the low-frequency oscillaltion amplitude looks like it starts out large and maybe decays linearly (on this time range), so shouldn't the cut reflect that better. Could this artifact be a result of the CWT process compared to FFT?

• This case is obvious but it helps write better answers to include data (e.g. Google Drive, Dropbox, ufile.io) Commented Jun 4, 2023 at 18:44
• Labeling also needs work. Matlab's cwt isn't linearly spaced, and linear spacing is awful for CWT. The time axes sometimes go below zero, sometimes not. This should either be fixed or clarified in the question. Also the LF decays linearly over an even longer duration than HF, so the question could be a bit more precise. I won't be answering without data, but maybe someone else will. Commented Jun 5, 2023 at 9:47

Looking at all of the four figures you provided, I think your CWT analysis result looks OK and reasonable. As shown in the second figure, near the left end, a narrow vertical bright beam there indicates a low frequency (LF) tone decays slowly. This is well consistent with the last figure, and with the waveform shown in the first figure, since the LF tone shown in the first figure indeed decays much slower than the high frequency (HF) tone, such that after the $$time\ index > 400$$ the LF tone is still quite strong, while the HF tone already almost disappears at all after the $$time\ index > 250$$. The last figure shows that the LF tone already starts to decay, but with a slower rate. If you have data for a longer time interval, you may see more further decay (of course, depending on whether the LF tone does really decay continuously).