On the application of a fast polynomial transform and the Chinese remainder theorem to compute a two-dimensional convolution

In this paper, a fast algorithm is developed to compute two-dimensional convolutions of an array of d
1
× d
2
complex number points where d
2
=2
^m
and d
1
=2
^m-r+1
for some
1\leq r \leq m
. This new algorithm requires fewer multiplications and about the same number of additions as the conventional FFT method for computing the two-dimensional convolution. It also has the advantage that the operation of transposing the matrix of data can be avoided.