T-cascade wave digital filters with zero sensitivity at each matching point for arbitrary transfer functions

Circuits that have zero amplitude sensitivity at each matching point are expected to have very low sensitivity in the passband; this is a preferable property. Wave digital filters (WDFs) having T-cascades structures can be pipelined to increase the processing speed. This paper shows the existence of T-cascade WDFs which have zero amplitude sensitivity at each matching point and which can realize arbitrary transfer functions. Especially, the case is considered where the port resistances are equal and thus multipliers to determine the ratio are not necessary. First, the constituent sections for such WDFs are shown. Each section simulates a fundamental section of doubly terminated reactance filters, and the separation method of such a section by factorization of scattering matrices is derived. Finally, the existence of WDFs which are structurally bounded even for coefficient quantization is shown.