Existence of structurally bounded wave digital filters for arbitrary transfer functions

Abstract

Structurally bounded circuits such as properly designed wave digital filters (WDFs) are known to have low sensitivity in the passband. Existing structurally bounded WDFs cannot always realize arbitrary transfer functions. This paper shows first the existence of structurally bounded WDF sections which correspond to reactance E sections and Richards sections and then derives their circuit structures. Such a natural assumption is made in this derivation that multiplier coefficients having the same nominal value continue to have the same value even under finite wordlength condition. Interconnections of the proposed sections cause delay-free loops, which can be removed using Kuroda's identity. Thus, it is shown that such WDFs that can realize arbitrary transfer functions while inheriting the structural boundedness of prototype reactance filters really exist.