Parallel FIR Filters Based On Modulo Arithmetic

Parallel FIR filters offer a powerful means of reducing the complexity of an FIR filter. This can be achieved with varying tradeoffs in the added latency. Unlike filtering based entirely on transforms whereby the latency exceeds the filter length, parallel FIR filters can operate with very low latency, while still offering significant reduction in the number of multiplications per output sample. Short transforms including the complex fast Fourier transform (FFT) and number theoretic transforms were originally proposed for use with parallel FIR filters. Though the complex FFT has been examined with limited gains for parallel FIR filters, number theoretic transforms (NTTs) have not been examined in detail. This paper presents results on using the NTT for parallel FIR filtering, which show significant benefits over the conventional decomposition techniques that use decimation factors that are powers of 2 and 3