Editing Infinite impulse response (section)

== Example ==
Let the transfer function <math>H(z)</math> of a [[discrete-time filter]] be given by:

:<math>H(z) = \frac{B(z)}{A(z)} = \frac{1}{1 - a z^{-1}}</math>

governed by the parameter <math>a</math>, a real number with  <math>0 < |a| < 1</math>.  <math>H(z)</math> is  stable and causal with a pole at <math>a</math>. The time-domain [[impulse response]] can be shown to be given by:

:<math>h(n) = a^{n} u(n)</math>

where <math>u(n)</math> is the [[Heaviside step function#Discrete form|unit step function]]. It can be seen that <math>h(n)</math> is non-zero for all <math>n \ge 0</math>, thus an impulse response which continues infinitely.

[[File:IIR-filter.png|880x720px|thumbnail|IIR filter example]]