For STFT, we impose window of certain size onto the original signal, then we perform fft on each window. The uncertanty about frequency and time is determined by the width of the window, however, I can't understand what is the point of having overlap windows...

If we have a signal, for instance, why can't we just divide the signal into 6 trunks (non-overlapping window), and then we perform fft on each of those trunks?

Maybe let me make it more clearly in my application. I am going to mostly dealing with 60Hz power line wave, and occationally, we want to monitor the 180Hz transient effect at the power line. Since the signal will be mostly periodic, should I use window then?


1 Answer 1

  1. We always want to apply some kind of a window function in order to minimize the effect of leakage. This makes rectangular window (lack of any windowing) case never used, this is why:

  2. Any tapering function used is almost always decreasing to zero at boundaries. enter image description here

This is why we are losing some data. In order to retrieve that somehow you will usually do 50% of overlap when processing. This will retrieve whatever was in between.

enter image description here

  1. Another thing is that if you apply the Inverse STFT, you should use complementary window, that is summing to 1, i.e. Hanning with 50%.

Finalising - yes, you should pretty much always use windowing in your applications.

For more comprehensive informations please refer to great white-paper:

Heinzel G. - Spectrum and spectral density estimation by the DFT, including a comprehensive list of window functions and some new flat-top windows

  • $\begingroup$ Thank you very much for your help! The matlab algorithm that I am looking at actually start 1st window (with its centre at the beginning of the time axis, but in your drawing it is the detail of first window. Can I assume that the reason they do this because they don't want to lose the information at the beginning of the time axis ? $\endgroup$
    – kuku
    Nov 25, 2014 at 16:00
  • $\begingroup$ Picture is only exemplary. You can see that there are no values on time axis. Way you describe is perfectly OK. Anyway it's just an addition of one extra frame. $\endgroup$
    – jojek
    Nov 25, 2014 at 16:59
  • $\begingroup$ Read the paper. Read the paper. Read the paper. Section 12. That is all. $\endgroup$
    – Andy Piper
    Aug 20, 2019 at 17:11
  • $\begingroup$ @AndyPiper: you mean 10, right? $\endgroup$
    – jojek
    Aug 20, 2019 at 18:06
  • $\begingroup$ Section 12 is a cookbook for all of this stuff and the best place to start in my view. Section 10 is specifically about overlap. But it's all great :) $\endgroup$
    – Andy Piper
    Aug 21, 2019 at 8:12

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