Fast filter bank (FFB)

The sliding fast Fourier transform (FFT) filter bank has an exceedingly low complexity of one multiplication per channel per sample. However, its frequency selectivity and passband response are poor. It is shown that the sliding FFT filter bank is in fact a particular member of a new family of fast filter banks (FFBs). In the case of FFT, each cluster of butterflies can in fact be derived from a pair of complementary two-tap (i.e. first-order) prototype FIR filters. The poor selectivity and degraded passband response of the FFT filter bank is a direct consequence of the poor frequency response of the prototype first-order filter. It is shown that by increasing the order of the prototype filters, it is possible to implement a filter bank with arbitrarily good selectivity and flat passband response. The FFB retains the low-complexity feature of the FFT. Because of its very much improved frequency response characteristics, the FFB be suitable for use in many applications where the FFT filter bank is unsuitable.<>