M. Abozahhad et al., ARBITRARY AMPLITUDE AND LINEAR-PHASE APPROXIMATIONS FOR NON-PROTOTYPELADDER AND LATTICE WAVE DIGITAL-FILTERS, International journal of circuit theory and applications, 24(6), 1996, pp. 605-620
Two different approaches are introduced for the design of non-prototyp
e 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 phas
e correction of a minimum phase lattice (or ladder) WDF designed to sa
tisfy the amplitude specifications in the three bands. In the second a
pproach the amplitude and phase requirements are approximated simultan
eously. It is devoted to the design of a lattice WDF that is construct
ed from the parallel arrangement of two allpass subfilters. The design
procedure relies on preconstructing one of the subfilters to have exa
ct linear phase at all frequencies and constructing the other to inter
polate 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 am
plitude specifications in the passband and stopband and phase specific
ations in the passband are also considered as special cases. Design ex
amples are presented to show the efficiency of the two methods.