Application of Two-Channel Prediction Filtering to the Recursive Filter Design Problem

Abstract

In the recursive filter design problem, we are given a finite segment of a causal filter,

$$H\left( Z \right) = {h_0} + {h_1}Z + \ldots + {h_{N - 1}}{Z^{N - 1}},$$

and it is desired to approximate the filter by a recursive filter of the form

$$G\left( Z \right) = B\left( Z \right)/A\left( Z \right)$$

where

$$\begin{gathered}B\left( Z \right) = {b_0} + {b_1}Z + ldots + {b_m}{Z^m} \hfill \\ A\left( Z \right) = 1 + {a_1}Z + \ldots + {a_n}{Z^n} \hfill \\ \end{gathered}$$

.