The optimal direct design of bandpass wave digital ladder filters for distinctly specified amplitudes in the two stopbands

The paper presents an optimal and direct complete design method for bandpass wave digital filters (WDFs) having ladder structures and approximating different minimum losses in the two stopbands. Moreover, the resulting loss characteristic is restricted to be equiripple in the three bands, i.e., it has the same features of elliptic response. The approximation is carried out directly without applying frequency transformation techniques. It relies on applying interpolation techniques combined with the Remez-exchange algorithm. The resulting transmission function is synthesized by successive partial extraction of the poles at zero and infinite reference frequencies from the successive resulting impedance functions followed by successive extraction of the finite transmission zeros from the remaining admittance functions. The wave digital realization is finally obtained by applying three-port series and parallel adaptors.