3.4. Introduction to digital filtering
We suppose again that θ = 1.
Given a WSS process X
and a sequence of real numbers h = {hj ∈ 
|j ∈ }, we are interested in the operation which at X makes a new process Y correspond, defined by:
(h 0T0 is also denoted as h1 where 1 is the identical mapping of L2 in L2).
In what follows we will still assume that 
; this condition is generally denoted h ∈ 
1 and is called (for reasons which will be explained later) the condition of stability.
DEFINITION.– We say that the process Y is the transform (or filtration) of the process X by the filter and we write =
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