If a normal filter can remove non damaging cycles from a signal for fatigue analysis why WT and CWT?

Hi All

what is the point of using Morlet Wavelt and CWT that eventually work as a normal filter function to reduce and omit the non damaging cycles from a signal ?

[Sindar]

This sounds like classwork. If not, you should ask the person who made the statement that you should use CWT

[farzad]

Please don't listen to your inner voice. Also that person you claim, does not exist. I am also not a student, so no class work.

by "should", I was asking and questioning about developing and possible advantages of CWT method. so if you know that, I will be eager to hear that

[Sindar]

In that case, you may get more replies if you give more information. I'm familiar with CWT, but don't understand quite what your process would be. Are you simply applying CWT, then extracting a range of desired frequencies?

[farzad]

well no I was just reading some articles and got to know that this method exits. So I don't understand what you mean by extracting a range of desired frequencies. What I know is that it eventually works like a filter with different window lengths? but I am not sure if we should be cautious about choosing the parameters for CWT to avoid filtering too much, or if we still need to check if we need less or further filtering

[farzad]

So I hope I have been clear in question

[farzad]

May I ask why you gave up this question ? I was hoping to receive some answer

[Sindar]

Sorry, didn't get alerts on comments, and forgot to check my activity till now. I think I understand now.

The point of CWT is to simultaneously present frequency and time information. So, it can answer questions that the original signal (time domain) or the frequency spectrum cannot. For example:

• What frequencies are present at the start of the signal?
• When does the highest frequency appear at appreciable strength?

There are other methods to access this information. The simplest is to apply a time domain window to your data, then FFT. Then repeat with windows centered at different times. Stacking these frequency spectra (from time-windowed data) will give you a similar picture to CWT. Likewise, you could take frequency data, apply rolling frequency filters, and iFFT to the time domain. This method is easy to code up and conceptualize, but has issues with normalization and resolution. CWT is designed to resolve them, partially by changing the window as a function of the frequency you are trying to resolve. Thus, CWT "works like a filter with different window lengths".

In my experience (in laser physics), CWT is used as an analysis tool (producing plots like this one from the CWT documentation), and is quite a good one (though it often produces plots which are not so easily parsed). I have not seen it used to extract data for further use. While the data is accessible, I am not sure how the particular numbers relate to a simple time or frequency filter

[farzad]

Thank you very much. May you tell me how should I choose the window size in this method ? have you used it in MATLAB ?

[Sindar]

I use an older CWT function that I don't recommend (just not worth my time to switch over at this point). But, generally, you'll be looking at some sort of "time-bandwidth product" parameter. This doesn't correspond directly to a window size (since that depends on the frequency), but it does allow you to tune whether you get more resolution in the frequency or time axes. Generally, my suggestion would be to start with the default, then explore from there. Usually, you'll get very sharp vertical lines if too low, sharp horizontal lines if too high, and blobs when you're in the generally useful region.

(there are ways to predict the value you'll need, but it depends on your frequency scale and which wavelet you're using, and is usually easier to explore first)