Stability
The transfer function allows us to judge whether or not a system is bounded-input, bounded-output (BIBO) stable. To be specific, the BIBO stability criteria requires that the ROC of the system includes the unit circle. For example, for a causal system, all poles of the transfer function have to have an absolute value smaller than one. In other words, all poles must be located within a unit circle in the -plane.
The poles are defined as the values of which make the denominator of equal to 0:
Clearly, if then the poles are not located at the origin of the z-plane. This is in contrast to the FIR filter where all poles are located at the origin, and is therefore always stable.
IIR filters are sometimes preferred over FIR filters because an IIR filter can achieve a much sharper transition region roll-off than FIR filter of the same order.
Read more about this topic: Infinite Impulse Response
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