Hanning & Hamming Windows in MATLAB: Why the Discrepancy?

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SUMMARY

The discrepancy between the Hanning and Hamming windows in MATLAB and their theoretical definitions arises from the formula used. The Hanning window is defined as 0.5 + 0.5*cos(2*pi*n/N) for n in the range [-(N-1)/2, (N-1)/2], where N is an odd number. However, MATLAB's "hanning" and "hann" functions yield results that differ slightly from this formula. Adjusting the denominator to (N-1) resolves this discrepancy, aligning MATLAB's output with the theoretical expectations.

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truva
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Hi all

As far as I know Hanning window is defined as the following:
.5+.5*cos(2*pi*n/N) and n is between [-(N-1)/2,(N-1)/2] here N is odd number.

MATLAB functions "hanning" with symetric or periodic options or "hann" do not match with the results of the above formula. There is always a slight annoying difference !

Do you know the problem?

(Same thing for Hamming window)
 
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As I understand the book is wrong (Notes On Digital Signal Processing by C. Britton Rorabaugh). If I replace the N by (N-1) in the denumerator of the formulation which is 5+.5*cos(2*pi*n/(N-1)), the results coincide exactly with that of MATLAB.

Thank you for the link.
 

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