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IS there a Matrix form of the STFT that could be applied to a signal directly, as in the case of DFT? We know the matrix structure of the DFT Matrix. Can we derive that somehow for a STFT Transform? The parameters that I wish to use are N = signal length R = frame length overlap = 50% DFT length = K

Attempt: I have tried to represent the DFT blocks along a diagonal with 50% overlap between the blocks. Each of the DFT Block will be multiplied by a diagonal block of the same size consisting of the window coefficients. Am I heading in the right direction?

Any directions or suggestions would be helpful. Thanks!!

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  • $\begingroup$ Sounds like you're heading in the right direction. Though, usually, the STFT will be there square of the DFT of each frame. $\endgroup$ – Peter K. Mar 27 '14 at 19:26
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For an overlapped STFT (overlap > 0), the output vector will be larger than the signal input vector, so the matrix form will not be square.

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  • $\begingroup$ That is fine. My aim is not to have the matrix and then multiply by the signal to get the STFT. My aim is just to obtain a matrix of basis vectors of STFT. Any hints for that? $\endgroup$ – AAP Mar 27 '14 at 22:35

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