Mathematical definition of the Short-time Fourier Transform (STFT) is given by
The window used in the STFT, , must satisfy the Constant
Overlap-Add (COLA) property:
If COLA is satisfied, then the sum of successive DTFTs over time
equals the DTFT of the whole signal , that is:
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Rectangle window is COLA if there is no overlap. Bartlett window, and all the Hamming family are COLA with 50 % overlap (when end points are handled correctly).