Prototype reference transfer function parameters in the discrete-time frequency transformations

A direct discrete-time frequency transformation technique is presented with which it is possible to transform a prototype normalized lowpass reference transfer function into a denormalized lowpass (LP), highpass (HP), bandpass (BP), or bandstop (BS) transfer function. The salient feature of the proposed technique is that it permits prescribed values to be assigned not only to the passband edge(s) but also to the stopband edge(s) of the required denormalized transfer functions. In addition, it permits one degree of freedom in the determination of the passband edge and the stopband edge of the lowpass reference transfer function. This degree of freedom has been exploited to derive the passband edge and the stopband edge of the reference transfer function for the important class of denormalized LP, HZP, BP, and BS transfer functions with elliptic magnitude-frequency characteristics