Harmonic scheduling of linear recurrences in 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, we need to effectively parallelize the linear difference equations used to describe digital filters - a difficult task due to the recurrences inherent in the data dependences. We 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 us to derive a parallel schedule with minimum control overhead, given an execution time with resource constraints. We also present a Harmonic Scheduling algorithm that generates optimal schedules for digital filters described by second-order difference equations with resource constraints