IIR filter feedback can cause instability unless poles stay inside the unit circle
Evidence
It is different from an FIR filter in that there are feedback paths through multipliers an. An IIR filter may be unstable if it is not designed properly, which means that it can produce arbitrarily large output values for a finite input signal if a frequency is exponentially amplified in the feedback structure. The stability criterion for an IIR filter is that the poles of the transfer function, that is, the roots of the denominator polynomial of Equation (3.32), must be inside the unit circle on the complex plane |z| < 1. The zeros (roots of the numerator) don’t have such a limitation. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 426
Categorization
Category: Definitional Content
- DEFINE: Clear mechanical explanation of why feedback filters can blow up and what the stability criterion actually is.