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I am new to the wavelet field, and I am working with ultrasound signal. For my study, I needed to measure material using the pulse echo reflection method.

Basically, when the transducer transmits the signal, the signal will reflected back to the transducer. If material has a thickness, the signal will reflected for two sides which are the front and back. After receiving both signals, I need to differentiate both of them, however the received signals are overlayed.

I think by using a wavelet method, I can differentiate the signal, but the result that I got is unclear. Can anyone explain about this result? Is it that both signals can be differentiated?

enter image description here

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  • $\begingroup$ I'm not sure wavelets (i.e. the scalogram) is suitable for what you need. If your main application is really determining the delay between the echoes then you should either look at a spectrogram with constant time resolution that you tune to resolve the echoes, or you should perform an autocorrelation analysis. What did you choose wavelets to start with? $\endgroup$ – Jazzmaniac Dec 4 '13 at 10:30
  • $\begingroup$ Thanks mr jazzmaniac,is it scalogram can differentiate the both signals. Because, now i am still confusing to determine the correct echo.thanks $\endgroup$ – Mr.Own Dec 4 '13 at 11:16
  • $\begingroup$ I wouldn't be able to discriminate echoes from this scalogram. $\endgroup$ – Jazzmaniac Dec 4 '13 at 14:29
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From what I can see you are not trying to detect defects. For defect detection (CM,Inspection) wavelets are really popular and they had and still has been used extensively. I am working in the same field for a while but from what I can understand, you are trying to measure the thickness of the material.

In any case, I couldnt quite understand your problem but I strongly advise you to go for spectrogram first. Scalogram is inherently better in terms of resolution (both in time and frequency) but it might be a bit tricky to understand scale-frequency relation as opposed to spectrogram.

Based on your plots, wavelet transform is picking up quite a few of wavelets. This probably is due to the fact that your signals are overlayed. You might want to seperate them. You might also want to go for different wavelets and decomposition levels, I personally know mexican hat and db mother wavelets can provide good results for NDT applications, both for denoising and transforms.

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  • $\begingroup$ It's certainly not correct to say that wavelets (or the scalogram) has a better resolution in time or frequency as other methods, specifically the spectrogram. The resolution is determined by the time frequency tradeoff that is constraining all linear methods. The wavelet transform just uses a different trade-off, giving better frequency (but worse time) resolution at low frequencies. The spectrogram has the advantage that you can easily tune frequency and bandwidth independently. $\endgroup$ – Jazzmaniac Dec 4 '13 at 18:42
  • $\begingroup$ @Jazzmaniac that's exactly what I tried to say, but apparently i thought faster than i wrote. I tend to use this especially if I am looking for high frequencies, for it gives (let's say wavelet transform vs FFT rather than scale-spectro) better (or more precise) time resolution at higher frequencies. Let's call it a slip of mind, thanks for the correction for the OP though. $\endgroup$ – SimpleMan Dec 4 '13 at 21:14
  • $\begingroup$ Hello bro @Jazzmaniac and SimpleMan, Thanks for your advice, i just want to know whether spectogram same with short time fourier transform. $\endgroup$ – Mr.Own Dec 5 '13 at 2:58
  • $\begingroup$ yes, it's the same thing (at least usually). $\endgroup$ – Jazzmaniac Dec 5 '13 at 7:44

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