Harmonic scheduling of linear recurrences for digital filter design

Linear difference equations involving recurrences are fundamental equations that describe many important signal processing applications. For many high sample rate digital filter applications, it is necessary to effectively parallelize the linear difference equations used to describe digital filters. This is difficult because of the recurrences inherent in the data dependences. The authors present a novel approach, harmonic scheduling, that exploits parallelism in these recurrences beyond loop-carried dependencies, and which generates optimal schedules for parallel evaluation of linear difference equations with resource constraints. This approach also enables the derivation of a parallel schedule with minimum control overhead, given an execution time with resource constraints. A harmonic scheduling algorithm is presented to generate optimal schedules for digital filters described by second-order difference equations with resource constraints