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  cohere(x,y,M) computes the coherence function using successive DFTs of length with a Hanning window and 50 overlap. (The window and overlap can be controlled via additional optional arguments.) We see a coherence peak at frequency cycles/sample, as expected, but there are also two rather large coherence samples on either side of the main peak. These are expected as well, since the true cross-spectrum for this case is a critically sampled Hanning window transform. (A window transform is critically sampled whenever the window length equals the DFT length.)