Feedback (IIR) filters can become unstable, while feedforward (FIR) filters cannot

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

• DEFINE: Clarifies why IIR filters risk instability through feedback poles while FIR filters are inherently stable.