The computational complexity of running FIR (finite-impulse response) and IIR (infinite-impulse response) filtering using multirate filter banks is considered. No restrictions are put on signal, filter, or block lengths. It is shown how to map long running convolutions into smaller ones by using filter banks based on aperiodic convolution algorithms and short-time Fourier transforms. With the proposed approach, good tradeoffs among computational complexity, system architecture, and input-output delay are achieved