**3.6. Exercises for Chapter 3**

*Exercise 3.1.*

Study the stationarity of the Gaussian process

*X* ∼ *N*(*m*(*K*), min(*j*, *K*)) where *E*(*X*_{K}) = *m*(*K*) is constant.

*Exercise 3.2.*

We are considering the real sequence *h*_{n} defined by:

1) Determine the convergence domain of the Laurent series .

2) If *h* = {*h*_{n} |*n* ∈ } is a digital filter, determine its transfer function *H*(*z*) by clarifying its definition domain.

*Solution 3.2.*

The series converges if and if |z| < 4, thus in the annulus .

The series converges if |z| > 2 and if |z| < 1/4, thus in the annulus

In *K′*: .

*Exercise 3.3.*

Develop *H* (*z*)= in series (of Laurent) of ...