In the corresponding paper, a generalized Fourier transform is introduced
and its corresponding generalized Poisson summation formula
is derived.
For discrete, Fourier based, signal processing, this
formula shows that a special form of control on the periodic repetitions
that occur due to sampling in the reciprocal domain is possible.
The paper is focused on the derivation and analysis of
a weighted circular convolution theorem. We use this specific result
to compute linear convolutions in the generalized Fourier domain,
without the need of zero-padding. This results in faster, more resource-
efficient computations.
Related publications
A Generalized Poisson Summation Formula and its Application to Fast Linear Convolution J. Martinez; R. Heusdens; R.C. Hendriks; IEEE Signal Process. Lett., Volume 18, Issue 9, pp. 501-504, 2011. DOI: 10.1109/LSP.2011.2161078 document
