Summary: IEEE SIGNAL PROCESSING LETTERS, VOL. 9, NO. 7, JULY 2002 211
An Improved Toom's Algorithm for Linear
Convolution
A. Elnaggar, Associate Member, IEEE, and M. Aboelaze
Abstract--This letter presents an improved Toom's algorithm
that allows hardware savings without slowing down the processing
speed. We derive formulae for the number of multiplications and
additions required to compute the linear convolution of size =
2 . We demonstrate the computational advantage of the proposed
improved algorithm when compared to previous algorithms,
such as the original matrix­vector multiplication and the FFT
algorithms.
Index Terms--Convolution, permutation matrices, shuffle net-
works, tensor products, Toom's algorithm.
I. INTRODUCTION
CONVOLUTION is a very important operation in signal
and image processing with applications to digital filtering
and video image processing. Many approaches have been sug-
gested to achieve high-speed processing for linear convolution
and to design efficient convolution architectures [1]­[5].

Source: Aboelaze, Mokhtar - Department of Computer Science, York University (Toronto)

Collections: Computer Technologies and Information Sciences