Suppose we have two sequences $x[n]$ of length $L$ , and $y[n]$ of length $P$. If we are doing a $L$ length circular convolution between the two sequences ($L>P$), how many of the resultant samples will be uncorrupted, i.e. same as linear convolution values ?

I think by intuition it should be $P-1$, but I'm not sure.


assuming $y[n]$ is padded with $L-P$ zeros (to make it the same length as $x[n]$ and your circular convolution length), then the number uncorrupted samples is $L-P+1$.

you might want to Google "Overlap Save" (OLS, a better name i have read is "Overlap-Scrap"), which is directly about this issue of uncorrupted samples in circular convolution. the alternative is "Overlap Add" (OLA) which has no corrupted samples, but you have to overlap the tails of each block and add them.

this is well covered in books like O&S.


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