A pipelined tree machine architecture for computing a multidimensional convolution

In this paper, a technique is proposed to decompose a two-dimensional (2-D) cyclic convolution of two
d_{1} \times d_{2}
arrays, where
d_{2} = 2^{m}
with
m > 1
, into many identical and independent 2-D cyclic convolutions of smaller size. Using this technique and the fact that fast polynomial transform (FFT) exists when
d_{1}=2^{m-r+1}
for
1 \leq r \leq m
, a pipelined tree machine architecture composed of modular FPT, FFT, and Chinese Remainder Theorem (CRT) computational units is then developed to efficiently compute a 2-D cyclic convolution. Finally, the extension of this tree machine architecture to efficiently compute a multidimensional cyclic convolution is discussed in this paper.