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I tried to find the answer by my own but unfortunately I couldn't.

Let's say I have the discret values of a signal which is 10s long.

What is the FFT which is performed on a sliding window with time?

What is the difference to the FFT, where I get the frequency spectrum of the signal?

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If you have the samples of a signal of length $L$ (corresponding to 10s analog duration for example) and want to analyse its spectrum, then you can peform an $L$ point DFT/FFT on the whole data at once.

This would provide you the maximum spectral resolution but minimum temporal resolution; i.e., time locality of the events are mainly lost (or better become obscured in the phase spectrum).

If you wish to sacrifice some spectral resolution but increase the temporal instead, then you can analyse the signal in small blocks (overlapping chunks) and move the block window in time to observe the change in the local spectral behaviour. This motion of the analysis window is referred to as sliding action. And the analysis is essentially a sliding window analysis, aka short-time Fourier analysis, windowed Fourier analysis etc.

Note that for various reasons it's best to use some weighting within windowing before the DFTs are applied.

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  • $\begingroup$ Thank you very much @Fat32. So, to fully understand this, if L=1000 I do split it in lets say ten 100 chunks, apply a weighting window (e.g. hamming) on this chunks ... but now I have two questions again : 1. How to decide the overlapping 2. Do I now have the spectrum of 10 chunks? If there is a source I could read this in detail (maybe with examples) I would be really grateful! $\endgroup$ – OcK May 6 at 20:29
  • $\begingroup$ there are trade-offs in deciding the length of the window. And overlapping amounts of %25 to %50 are very common. The shorter the overlap, the more the jumps between the chunks and also more efficient to compute. If too much overlap, you would get little extra benefit at a demanding computational cost. $\endgroup$ – Fat32 May 6 at 21:05
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    $\begingroup$ one can even do 75% overlap. or 87.5% overlap. if you keep your phases in line and use a correctly-scaled complementary window (like Hann), this results in a really smooth STFT. conceptually you can overlap all samples except one. so the window slides exactly one sample for each input sample and this whole DFT and inverse DFT happens for every sample. really computationally costly, but about as smooth as you're gonna get. $\endgroup$ – robert bristow-johnson May 8 at 20:00
  • $\begingroup$ thanx! that's what I wanted to say indeed ;-) $\endgroup$ – Fat32 May 8 at 20:01
  • $\begingroup$ what I don't follow about the sliding window approach is that you're gonna get a different DFT ( or STFT ) as the new samples arrive so which one is correct ? This is a well known problem in time series where you want to estimate something so, as new data comes in, you use a rolling window and the estimate changes. so which estimate is correct ? no one knows. or maybe the whole data should be used. there is no answer, atleast in the time domain. $\endgroup$ – mark leeds May 9 at 2:55

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