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Hello I'm reading the following document to better understand windowing and how to use it.

"Spectrum and spectral density estimation by the Discrete Fourier transform (DFT), including a comprehensive list of window functions and some new at-top windows."

You can find the file overhere

I try to reproduce their example (chapter 13) on audio signals but i have some questions. Just like the example i use the Hann(ing) window. with a overlab of 50% For reproducion i use python

Let say i have a typical Audio signal with a fs of 44100 Hz and a length of T = 5 sec. I have a window of 0.1 sec(neglecting the nice length of N). With the overlab i get an matrix of 100(Windows) X 4410 Samples.

I have two questions

  1. Normaly i see just a single Spectrum plot (exept STFT). How come i from a my set of spectra to a single spectrum? Like what Audacity have
    Averaging; summing; ... other

  2. what is the impact of changes in time at the resulting spectrum. Let say using a (measured) sweeping signal?

Hope that somebody can help me now

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  • $\begingroup$ please can somebody help me?? or tips for better question or split the question? $\endgroup$ – Jan-Bert Mar 3 '16 at 10:18
  • $\begingroup$ Is your doubt related to plotting spectrum(or spectrogam) for entire length of signal, and the effects of window length on spectrogram ? $\endgroup$ – arpit jain Mar 10 '16 at 8:20
  • $\begingroup$ the question is basicly... When have a large array of data with a relatively short Window. I get a lot of FFT frames. Is it possible to mix these frames together to a more narrow FFT and How do I sum up all these frames to make a single spectrum $\endgroup$ – Jan-Bert Mar 10 '16 at 11:33
  • $\begingroup$ I think there is some clarification needed, first of all if you know that your input signal is stationary, then you need not do windowing. and if your signal is non-stationary you should not expect summing-up/adding to get single spectrum, in this case you should observe spectrum for each window(of that particular time instant/window). $\endgroup$ – arpit jain Mar 10 '16 at 11:49
  • $\begingroup$ But how does software as Audacity, Ardour, Ableton or Logic pro handle this kind of information? This is always in some $2^N$ sample bins and i think also a window... That software is also not stationary and become one final spectrum. $\endgroup$ – Jan-Bert Mar 10 '16 at 19:45

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