A generalized class of lattice wave digital filters

The class of lattice wave digital (LWD) filters, which are constructed as a parallel connection of two all-pass branches, is extended beyond the known lowpass, highpass, bandpass, and bandstop designs. The goal is to generate a generic design procedure for LWD filters having an arbitrary number of interlaced passbands and stopbands such that such that in each passband and stopband the magnitude criteria are the most arbitrary. For this purpose, the overall design is governed by the phase response behaviors of the two all-pass filters and, in addition, the rules are established for the behavior of their unwrapped phase difference such that all the feasible patterns of phase transitions between consecutive bands are included. Among these patterns, only one results in the best LWD filter solution. These extensions provide significantly more degrees of freedom for synthesizing many novel LDF filters. Very concrete novel filters not being synthesizable using traditional techniques are bandpass and bandstop filters, for which the orders of both branches are the same, and, thereby, the overall order is two times an even integer. The above extended properties of LWD filters are brought to reality by properly generalizing the Remez algorithm proposed earlier by two authors of this paper for determining the above-mentioned phase difference such that it minimizes in the Chebyshev sense a given weighted error function on a close subset of [0, π]. Four examples are included to demonstrate the use of the proposed overall synthesis scheme and the novelty of the resulting LWD filters.