Filtering > a first order AR filter

Digital filters can operate in the space domain by using the convolution product. A sampled signal can be represented by a polynomial of variable z and/or by a set of coefficients. The convolution product of two signals is the product of the polynomials in z domain of these signals. All linear filters can be presented by the relationship between two polynomials in z.
A filter for whom the polynomial is a fraction, whose numerator is equal to 1, is an autoregressive filter or AR. In this section, we study the behaviour of a first order AR filter.