On unit element structures for wave digital filters

A design procedure is presented for unit element filters which consist of a chain of shunt capacitances separated by cascaded unit elements having the same characteristic impedance. Based on an equal-ripple characterization of the passband response and somewhat related to the Remez algorithm, it uses a symbolic analysis of the unit element filter to perform the necessary gradient computations. Closed-form expressions of the characteristic function for particular values of the capacitances yield excellent starting guesses to the iterative process. The present approach is shown to be superior to previous work which made use of the Fletcher-Powell algorithm. In particular, the obtained equal-ripple filters fulfill necessary conditions for optimal selectivity. In comparison with true ladder configuration, the resulting wave digital filter not only leads to higher hardware modularity but, in a wide range of passband ripples, it also displays much better selectivity for the same expense of multipliers.