Realization of arbitrary filters in the STFT domain

It is well known that FIR filters can be efficiently realized in the short-time Fourier transform domain, namely using sliding windows and FFTs. In some scenarios, however, the standard overlap-add or overlap-save block convolution algorithms may be impractical due to the need for large transforms to implement long filters. In this paper, we show how to realize arbitrary FIR and IIR filters in an STFT framework whose block size, hop size, and transform size are not constrained by the target filter response. First, we review a subband filtering approach which enables implementation of arbitrarily long FIR filters in such a fixed-size STFT system via an overlap-add decomposition of the target filter impulse response. We then extend the subband filtering framework to the case of IIR filtering: first, we show how to map a single-pole filter into single-pole subband filters; then, we show how to map any arbitrary IIR filter into a subband filtering scheme. These approaches are useful for applications such as filter realization in modular frequency-domain systems, filter implementation on restricted hardware, compressed-domain processing in frequency-domain coding systems, and subband adaptive filtering.