General spectral transformations for digital filters

Constantinides [1] gave a method of transforming a prototype low-pass digital filter into a high-pass, bandpass, or bandstop filter by conformally mapping the complex variable Z^-1. We generalize here his method to transformations from prototype low-pass filters to filters containing any number of pass- and stopbands. The computation procedure involves only the solution of a set of simultaneous linear equations, the number of which is related only to the number of band-edges and not to the order of the prototype filter.