Wave‐digital cascade synthesis

Abstract

SUMMARYThe purpose of this paper is to demonstrate the possibility of a wave-digital cascade synthesis. Each section, reciprocal as well as non-reciprocal, being for instance the result of a cascade synthesis based on the factorization of the transfer matrix of an analogue lossless two-port network, is translated into a wave-digital realization. Except for the zero-order sections, it is shown to be sufficient that each section is cascaded with one unit-element in order to obtain an equivalent network which can be translated into wave-digital form. It gives some insight in the price to be paid in terms of complexity of the realization if a perfectly general transfer function is to be realized in wave-digital form.By some examples it is shown how each structure which has been introduced can be 'passified' if it cannot be realized by a lossless structure.

A general realization method for wave digital filters

“…The corresponding scattering coefficients and S22 derived from (4) In order to avoid delay-free loops,5 6 the constant term in the numerator of either Sll(Z) or 522(Z) must be set to zero. Using this condition, the relationship between R1 and R2 in terms of the impedance function (7) can be easily derived.…”