Question

the main reason for instability in an iir filter is: a) high order of the filter b) low order of the filter c) poles located inside the unit circle in the z-plane d) zeros located outside the unit circle in the z-plane

Answer 1

Instability in an IIR filter is primarily caused by poles located outside the unit circle in the z-plane. While high order filters may be more sensitive, the direct cause of instability is the pole placement. Zeros affect the frequency response but not stability.

Step-by-step explanation:

The main reason for instability in an Infinite Impulse Response (IIR) filter is c) poles located inside the unit circle in the z-plane. When designing IIR filters, it is crucial to ensure that all poles of the filter are inside the unit circle on the z-plane for the system to be stable. If the poles lie outside the unit circle, the filter would show an unbounded response to a bounded input, which is an unstable behavior in the time domain. On the contrary, the location of zeros does not directly influence stability, although they do affect the frequency response of the filter.

High order filters (a) tend to be more sensitive to coefficient quantization, which might lead to a slight shift of poles and potential instability, but this is a different concern from the fundamental issue of where the poles are located. Low order filters (b) are less complex and generally more stable, provided their poles are correctly positioned inside the unit circle.