Bidirectional systolic arrays for digital recursive filters

Bidirectional systolic convolution arrays have interesting features for the realization of recursive filters, but are inefficient in what concerns the throughput rate and the utilization of computational resources. In this paper, we derive efficient bidirectional systolic arrays for uni-dimensional and two-dimensional recursive filters, by interleaving the computation of non-recursive and recursive parts of the filters and by using iteration and retiming techniques. These systolic arrays require a minimum number of multipliers and allow a sampling rate that is bounded by twice the time of a multiplication. We also discuss the design of fine-grain bidirectional systolic arrays, for applications that require high throughput rates.