1
$\begingroup$

For now I use FFT to analyze the response of an electrical system to some transient signal. The transient signal is $x(t)$, which translates to $X(w)$ in the frequency domain. On the other hand I have $H(w)$, the response of my system to a unit input signal. Then to get the response of the system to the input $X(w)$ I simply do $X(w)*H(w)$; I then get $Y(w)$ and finally $y(t)$ follows from IFFT.

My question is, would wavelet be a better way of doing this? I know that wavelet analysis is usually very good for transient signal analysis, but I wonder if they apply when one want to get the response of a system to an transient input?

$\endgroup$
  • $\begingroup$ I'm not sure you would have a nice, closed form solution like you have here with wavelets. Is there some specific problem with your current method that you are trying to address other than wanting something better in some vague transient sense? $\endgroup$ – Bjorn Roche May 2 '14 at 18:04
  • $\begingroup$ Basically I identified two flaws using fft: the computational cost is higher than the one achievable with wavelet (O(n log(n)) vs O(n)); and I may not need all the computed frequencies to get a clean output (i.e. an y(t) that makes sense without getting in to many details); so I thought the coarse/details approach of wavelet decomposition might be useful for this problem. If this is the case, I will then ask: how can I get this transfer function from wavelet decomposition? Is this even possible? $\endgroup$ – CTZStef May 2 '14 at 18:16
  • $\begingroup$ A better way of doing what exactly? Getting $y(t)$? Or are you trying to process the transformed data somehow? $\endgroup$ – AnonSubmitter85 May 2 '14 at 20:34
  • $\begingroup$ Nope, simply get $y(t)$ $\endgroup$ – CTZStef May 3 '14 at 1:33
  • $\begingroup$ The answer then depends on your processing requirements. What's your data size? Is this a real-time system that needs to perform this calculation so many times per second/minute/day/whatever? And so on and so on. If I understand you correctly, all you want is $x(t) \ast h(t)$. You haven't provided enough information to help determine what the best way to calculate this convolution would be, nor what criteria would be used to decide what is meant by best. $\endgroup$ – AnonSubmitter85 May 3 '14 at 2:35
1
$\begingroup$

I'm very curious about your application of this, the reason for this is because I think I should remind you the conditions for the use of the Fourier transform.

Fourier transform is suitable for square integrable signals (finite energy) and also that are absolutely summable, and with this are my worries, when we deal with transient signals the system usually does not behave stationary, hence Fourier transform is not a suitable tool, and also is very common that the system is unstable and does not converge, that's the main reason for the use of the Z-transform, in order to analyze the stability of the system and once the system is stable then the frequency analysis is made by evaluating the Z-transform over the unit circle.

Wavelet sound like a suitable tool for doing the analysis but again, first you need to warranty the convergence if the signal in order to justify the use of the tool.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.