In a recent discussion Linear vs. Circular Convolution on avoiding circular convolution by FFT, it was shown that the FFT length for convolution purposes set should be = (data set 1)+ (data set 2) -1.
For example, the length of data set A and B is 1000 each. The FFT of linear convolution of A and B in Fourier domain should be FFT(A, 1999) x FFT(B, 1999).
If it is desired that we keep the original number of points as in A, one can trim the first 500 points in the beginning and 499 points at the end or one can discard the first 499 points and then remove 500 points at the end.
A similar problem can arise if the length of A and B is odd, say 1001 point. The convolution length would be 2001.
What is the correct approach for discarding the ends of a convolution?
MATLAB has a "same" option in convolution, but they don't mention how the points are discarded.