Robust simultaneous amplitude and phase approximations oriented to bandpass wave digital lattice filters

Abstract

A straightforward design method is delivered for bandpass wave digital lattice filters satisfying arbitrary amplitude and linear phase specifications. The optimality and efficiency of this method are ensured by two sources. On the one hand, the approximation is carried out directly without the need to apply frequency transformation techniques. On the other, the amplitude and phase specifications are approximated simultaneously. The approximation process is relying on the pre-construction of one of the two branch all-pass functions to exhibit exact linear phase. The other all-pass function is determined such that it controls the amplitude and/or phase responses in the passband and the two stopbands. Accordingly, the approximation problem is reduced to constructing a strictly Hurwitz polynomial specified by its phase within the Nyquist range. The approximation problem is solved by applying interpolation techniques combined with the iterative Remez-exchange algorithm. The realization of the resulting filter is carried out according to explicit formulae. The delivered method is applied through two examples illustrating its efficiency and reliability. © 1998 John Wiley & Sons, Ltd.