Definition:Linear Filter/Transfer Function

Definition
Let $S$ be a stationary stochastic process governed by a white noise process:


 * $\map z t = \mu + a_t$

where:
 * $\mu$ is a constant mean level
 * $a_t$ is an independent shock at timestamp $t$.

Let $L$ be a linear filter on $S$:

The operator:
 * $\map \phi B := 1 + \phi_1 B + \phi_2 B^2 + \cdots$

is the transfer function of $L$.