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I'm working with audio files and I have to find their long term average spectrum. Although I had an option available in the software Praat but I don't understand the algorithm of finding the spectrum. I need to understand it so I know the actual working and also implement it through MATLAB!

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Sounds like a conventional spectral analysis, just do an FFT over your entire audio file and you obtain an averaged spectrum of the file. A Fourier transform can be viewed as a set of band-pass filters with integration.

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