Coherent sampling is achieved by finding $M_cycles$ and $N_samples$ which satisfy the following equation.
fin/fs = Mcycles / Nsamples
where fin is the input frequency, fs is the sampling frequency , Mcycles is the number of cycles and Nsamples is the number of samples.
Why do we need Mcycles to be a co-prime number of Nsamples?
I have read a lot of tutorials but they say in order not to sample different cycles at the same position and thus generates unduplicated data for FFT. I am not sure it is the right reason. I feel it has something to do with avoiding aliasing for harmonics.
Does someone have a mathematical reason for choosing prime numbers?
Purely for the sake of #s: http://mathworld.wolfram.com/MersennePrime.html
http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html
As far as FFT (Radix-2) goes , normalization, also spectral independence .
Eg: http://www.mit.edu/~abari/Papers/ISSCC14.pdf
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