Turning Overlap-Save into a Multiband Mixing, Downsampling Filter Bank

1053-5888/06/$20.00©2006IEEE I n this article, we show how to extend the popular overlap-save (OS) fast convolution filtering technique to create a flexible and computationally efficient bank of filters, with frequency translation and decimation implemented in the frequency domain. In addition, we supply some tips for choosing appropriate fast Fourier transform (FFT) size. Fast convolution is a well-known and powerful filtering technique. All but the shortest finite impulse response (FIR) filters can be implemented more efficiently in the frequency domain than when performed directly in the time domain. The longer the filter impulse response, the greater the speed advantage of fast convolution. When more than one output is filtered from a single input, some parts of the fast convolution algorithm are redundant. Removing this redundancy increases fast convolution’s speed even more. Sample rate change by decimation (downsampling) and frequency translation (mixing) techniques can also be incorporated efficiently in the frequency domain. These concepts can be combined to create a flexible and efficient bank of filters. Such a filter bank can implement mixing, filtering, and decimation of multiple arbitrary channels much faster than direct time-domain implementation.