The design of nonuniform modulated filterbanks

We present an approach to nonuniform filterbank design based on modulated filters and the principle of adjacent channel aliasing cancellation. The approach is a generalization of pseudo QMF designs to nonuniform channel arrangements and the essential idea is to form nonuniform filterbanks from uniform sections joined by "transition" filters. All channel filters are formed by modulating lowpass prototypes. To meet the aliasing cancellation conditions, the transition filters are modulated from complex lowpass prototypes, although the resulting channel filters are still real. The approach provides a computationally simple method for designing filterbanks with large numbers of channels because of the fact that channel filters are modulated from a few lowpass prototypes and because the lowpass prototype designs can be scaled. That is, designs for narrow channel spacing can be produced from designs for wider channel spacing by interpolating the lowpass prototype impulse response. The development is limited to the design of nonuniform filterbanks with integer decimation factors, although we demonstrate that the technique can be used to produce excellent rational decimation factor designs by combining channel outputs using an inverse polyphase transform.