The feedback lattice filter forms, including the two-multiplier form a
nd the normalized form, are examined with respect to their relationshi
ps to the feedback direct form filter. Specifically, the transformatio
n matrix between the lattice forms and the direct form is dervied; par
ameter and state relationships between the lattice forms and the direc
t form are therefore obtained. An IIR filter structure-the cascade lat
tice IIR structure-is constructed. Based on this structure, three IIR
adaptive filtering algorithms in the two-multiplier form can then be d
eveloped following the gradient approach, the Steiglitz-McBride approa
ch and the hyperstability approach. Convergence of these algorithms is
theoretically analyzed using either the ODE approach or the hyperstab
ility theorem. These algorithms will then be simplified into forms com
putationally as efficient as their corresponding direct form algorithm
s. Relationships of the simplified algorithms to the direct form algor
ithms are also studied, which disclose a consistency in algorithm stru
cture regardless of the filter form. Three normalized lattice algorith
ms can also be derived from the two-multiplier lattice algorithms. Exp
erimental results show much improved performance of the normalized lat
tice algorithms over the two-multiplier lattice algorithms and the dir
ect form algorithms.