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On page 76 of the book Discrete Time Speech Signal Processing by Thomas F.Quatieri, the author states "shortening the window widens its Fourier Transform".

Can anyone explain why?

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As per my knowledge, you can use the context of Duality property of Fourier to understand this. So if you reduce the time window size then the spectrum (Fourier transform)should widen(Duality). Hope this helps!

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  • $\begingroup$ Hi: If you go to this link and scroll down to "fourier transform of the box function", it explains why quite clearly. thefouriertransform.com/transform/fourier.php#box $\endgroup$ – mark leeds Mar 7 at 3:12
  • $\begingroup$ @markleeds Very intuitive and clear explanation. Thanks! $\endgroup$ – Steven Chan Mar 7 at 6:04
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    $\begingroup$ glad to help. it's rare for me. note also that the link says that duality is something else but maybe it has two meanings ? $\endgroup$ – mark leeds Mar 7 at 18:59

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