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rldivide

inverse Fourier transform with windowing and 50% overlap

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Hello, I'm writing an application with discrete Fourier transform and windowing (blackman-harris, hanning, etc), with a 50% overlap from one to block to the next. So far, it's okay. Problems happen when I want to do the inverse transform, to get the original signal back: I do recover each block with its windowing, but I do not know how to mix them together (with a 50% overlap) to get the exact original signal. In my naivety I thought that if I rectified them to get a triangular window (0..0.5..1..0.5..0) they would mix perfectly, but they don't ! Thanks for clarifying...

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Overlap-add reconstruction is a common method. Each block is aligned after each other, and added where blocks overlap. With a proper window and overlap, this will perfectly reconstruct the original signal.

The cases with perfect reconstruction is where the overlapped windows add to a constant value. A Hanning window gives a perfect overlap-add reconstruction with 50% overlap, but a Blackman-Harris does not.

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