# Window function on large arays

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

• please can somebody help me?? or tips for better question or split the question? – Jan-Bert Mar 3 '16 at 10:18
• Is your doubt related to plotting spectrum(or spectrogam) for entire length of signal, and the effects of window length on spectrogram ? – arpit jain Mar 10 '16 at 8:20
• 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 – Jan-Bert Mar 10 '16 at 11:33
• 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). – arpit jain Mar 10 '16 at 11:49
• 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. – Jan-Bert Mar 10 '16 at 19:45