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Sampling a cosine wave of 10 Hz at Fs = 64 and number of samples Ns = 256 I setup my time vector for the cosine wave as n=(0:Ns-1)*(1/Fs)

If I change the sampling frequency from 64 to 64.0005 I get imaginary spectrum coming up from the quantization noise and actually having significant amplitudes. I also get this at 65, 66, 67, etc but not at powers of 2, ie Fs=128,256...

I thought it was because the signal was truncated, but I substantially increased the number of samples (Ns) and this had little to no effect in removing the imaginary components of the cosine.

Can someone please advise what the link here is?

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Yes that's called as the aperture effect and indicates that if the FFT window length (the aperture) coincides with an integer number of signal periods, then the resulting FFT spectrum will have no leakage artefacts (mostly having zeros, up to quantization noise, bins) and significantly nonzero bins only at the signal frequencies.

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