Synthesis and realization of generalized Chebyshev digital filters with minimum number of multipliers

Abstract

A synthesis procedure is presented for a class of wave digital filters designed with a minimum number of multipliers. The minimization is achieved by digitizing an appropriate reference analogue symmetrical ladder network having excellent characteristics. The network satisfies an odd-degree generalized Chebyshev response, having an even multiple of transmission zeros at a finite real frequency and the remainder at infinity. Each LC parallel/series resonant branch in the structure is treated as a four-port network and transformed into the appropriate wave digital adaptor with only one multiplier. Synthesizing the digital filter from both ends toward the middle results in a homogeneous structure with a reduced signal path and lowest overall number of multipliers.