\begin{definition}[Definition:Linear Filter/Transfer Function]
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 $S$:
{{begin-eqn}}
{{eqn | l = \map z t
      | r = \mu + a_t + \psi_1 a_{t - 1} + \psi_2 a_{t - 2} + \cdots
      | c = 
}}
{{eqn | r = \mu + \map \psi B a_t
      | c = 
}}
{{end-eqn}}
The operator:
:$\map \psi B := 1 + \psi_1 B + \psi_2 B^2 + \cdots$
is the transfer function of $L$.
\end{definition}