Realizable Filters and Differential Equations

Abstract

This lesson is a direct continuation of the last one. We are going to look for the causal solutions of a linear differential equation with constant coefficients; thus by assumption, the filter will be realizable (Section 34.2). For convenience we write the equation with b _q = 1:

$$\sum\limits_{k = 0}^{q - 1} {{b_k}{g^{(k)}}} + {g^{(q)}} = \sum\limits_{j = 0}^p {{a_j}{f^{(j)}}}$$

(35.1)

.