Multistage, multirate FIR filter structures for narrow transition-band filters

An FIR (finite impulse response) filter system which is capable of implementing virtually any practical low-pass and high-pass filter with as little as 50-60 multiplications per sample is presented. The method is based on multirate techniques and complementary filters. The principle and the necessary building blocks are briefly described. Practical design methods for optimization are presented together with design examples and plots of the multiplication rates. Aliasing and finite-wordlength effects are discussed. The resulting system, while having a remarkably low arithmetic complexity, will usually require somewhat more memory than a conventional optimum direct-form filter and a slight increase in the internal signal representations