Two different approaches are introduced for the design of non-prototype ladder and lattice wave digital filters (WDFs) exhibiting arbitrary amplitude in the baseband (passband, transition band and stopband) and linear phase in the passband. The first approach is based on the phase correction of a minimum phase lattice (or ladder) WDF designed to satisfy the amplitude specifications in the three bands. In the second approach the amplitude and phase requirements are approximated simultaneously. It is devoted to the design of a lattice WDF that is constructed from the parallel arrangement of two allpass subfilters. The design procedure relies on preconstructing one of the subfilters to have exact linear phase at all frequencies and constructing the other to interpolate an arbitrary phase at a set of frequencies distributed all over the baseband. The hidden relationship between the amplitude and phase functions of the filter is utilized to approximate both of them.
The approximation problem is solved by applying an interpolation technique combined with the Remez exchange algorithm. Prototype filters with amplitude specifications in the passband and stopband and phase specifications in the passband are also considered as special cases. Design examples are presented to show the efficiency of the two methods.