Synthesis of bireciprocal wave digital filters with equiripple amplitude and phase

In this contribution, robust simultaneous amplitude and phase approximations are delivered for bireciprocal wave digital filters exhibiting arbitrary amplitude and linear phase responses. Moreover, the resulting amplitude and phase characteristics are equiripple. The approximation is relying on translating the given amplitude and phase specifications into corresponding specifications for the difference and sum phase functions of the two branch bireciprocal polynomials. Consequently, these difference and sum functions are approximated in an alternative and iterative procedure such that they converge into their optimal behavior. Accordingly, the two branch polynomials are finally obtained and the synthesis of the filter structure in the wave digital domain is determined.