Synthesis of FIR lattice structures

The usual procedure for synthesising the Nth order digital FIR transfer function A_N(z) in which the constant term is unity and the coefficient of z^-N is -a_N(N) by a lattice structure fails if a_N(N)=±1. The author is concerned with a solution to this problem. It is known that under this condition. A_N(z) must be linear phase to be realisable by a lattice structure. A synthesis procedure is given for such an A_N(z). For a general nonlinear phase A_N(z) with a_N(N)=±1, an alternative synthesis procedure is also given in terms of parallel lattice structures