This is sometimes called acyclic convolution to distinguish it
from the cyclic convolution used for length sequences in
the context of the DFT . Convolution is cyclic in the time
domain for the DFT and FS cases (i.e., whenever the time domain has a
finite length), and acyclic for the DTFT and FT cases.3.6.
The convolution theorem is then
That is, convolution in the time domain corresponds to
multiplication in the frequency domain.
Proof: The result follows immediately from interchanging the order
of summations associated with the convolution and DTFT: