A Simple Derivation of the Spectral Transformations for IIR Filters

A simple method is given for deriving the spectral transformations for infinite-impulse response (IIR) filters, which can be used to transform a prototype low-pass (LP) digital filter to another LP, high-pass (HP), bandpass (BP), or band-stop (BS) digital filter with prescribed passband edge(s) and the same tolerances as those of the prototype. The method is based on a combination of bilinear transformation with the analog frequency transformation and is simpler—conceptually, as well as from the calculation point of view—than the conventional method based on all-pass transformation functions.