We all know that the convolution between a signal f(t) and the
Delta function D(t - t0) is to shift f(t) with t0 away. But, how could
we validate this property? Namely, how do we implement the
convolution between a signal f(t) and the Delta function D(t - t0),
where t0 is a shift constant.
I think, we can implement it in frequency space, but I don't know
how bu sample exp(-j w t0), which is the Fourier transform of Delta(t-t0).
I just got the answer this moring.
A reasonable interval for sampling Delta(t - t0) is 2*pi/N, where N denotes
the length of the signal f(t). It is effetive regardless of the sign of t0.