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Reducing Multiphase Multirate Arrays

Neil Dunstan

Department of Mathematics, Statistics and Computing Science,
The University of New England,
Armidale 2351, Australia.

neil@neumann.une.edu.au

Patrick M Lenders

Department of Mathematics, Statistics and Computing Science,
The University of New England,
Armidale 2351, Australia.

pat@neumann.une.edu.au

#### Abstract

Systolic arrays have proven to be a useful architecture for signal and
image processing tasks.
Techniques to derive special-purpose processing arrays from mathematical
formulations of problems have been developed successfully, especially for
cases where data dependencies are uniform. In recent times new architectural
forms have emerged from the basic systolic structure. Multirate and Multiphase
multirate arrays are systolic arrays through which variables may travel
at different rates. Precise specification of these arrays can be given in
the form of Systems of Sparse Uniform Recurrence Equations.
When the problem formulation
has just two or three indices the array is one or two dimensional.
Problems with more than three indices result in arrays of three or more
dimensions, which is not considered to be practical for implementation
as a special--purpose VLSI device, nor convenient
for mapping onto
typical general--purpose multiprocessor architectures.
In this paper, the synthesis procedure for Multiphase multirate arrays is
augmented for the case where the problem has four or more indices,
which is common in image processing. The
objective is to reduce the dimensions of a multiphase multirate array
while retaining its distinctive behaviour.

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