Optimal Filter Partitions for Real-time Fir Filtering Using Uniformly-partitioned Fft-based Convolution in the Frequency-domain

This paper concerns highly-efficient real-time FIR filtering with low input-to-output latencies. For this type of application, partitioned frequency-domain convolution algorithms are established methods, combining efficiency and the necessity of low latencies. Frequency-domain convolution realizes linear FIR filtering by means of circular convolution. Therefore, the frequency transform’s period must be allocated with input samples and filter coefficients, affecting the filter partitioning as can be found in many publications, is a transform size K=2B of two times the audio streaming block length B. In this publication we review this choice based on a generalized FFT-based fast convolution algorithm with uniform filter partitioning. The correspondence between FFT sizes, filter partitions and the resulting computational costs is examined. We present an optimization technique to determine the best FFT size. The resulting costs for stream filtering and filter transformations are discussed in detail. It is shown, that for real-time FIR filtering it is always beneficial to partition filters. Our results prove evidence that K=2B is a good choice, but they also show that an optimal FFT size can achieve a significant speedup for long filters and low latencies.