Synthesis of multirate VLSI arrays

Many applications in signal and image processing can be implemented on regular VLSI architectures such as systolic arrays. Multirate arrays, or MRAs are an extension of systolic arrays where different data streams propagate with different clocks. It is known that they can be modelled as systems of uniform recurrence equations over sparse polyhedral domains. Using well known linear index transformation rules for systems of affine recurrence equations, or SAREs, we show that MRAs constitute a particular proper subset of SAREs. We describe how an MRA can be systematically derived from an initial specification in the form of a mathematical equation. The main transformation that we use is dependency decomposition, and rue illustrate our method by deriving a hitherto unknown decimation filter array that improves upon the hardware cost of previously published filters.