II‐cascade wave digital filters that have zero sensitivity at each matching point and realize arbitrary transfer functions

Abstract

AbstractThe circuit with zero sensitivity at the matching points is desirable in the sense that a very low sensitivity can be expected in the passband. It should also be noted that the wave digital filter (WDF) with a II‐cascade structure has the advantage that the sensitivity in the stopband is lower than WDF with a T‐cascade structure. However, the synthesis method has not been known for WDF with a II‐cascade structure with the zero amplitude sensitivity at the matching points which can realize an arbitrary transfer function. This paper is an attempt to realize such a WDF.First, it is shown what type of sections should be used as the reference section of a doubly resistor‐terminated reactance filter. The two terminating resistances are set equal to avoid the situation where the sensitivity at the matching point turns out to be nonzero because of the effect of the terminating resistance ratio. Then the replacement of the multiplier is shown so that the forementioned state is maintained, even if the multiplier coefficients are quantized.It is shown that WDF exists corresponding to each section, where the forementioned replacement can be applied and the structural boundedness is retained even after the coefficients are quantized. As a result, it is shown that WDF actually exists with a II‐cascade structure with the zero amplitude sensitivity at the matching points which can realize an arbitrary transfer function.