Numerically Stable IIR filter

1. Can IIR filters be stable?
2. Why are IIR filters not stable?
3. Which is the best IIR filter?
4. Which filters are inherently stable?

Can IIR filters be stable?

The stability of an IIR filter can be analyzed by the zero-pole plot of the filter's transfer function. A digital filter is stable if and only if all the poles of the irreducible filter transfer function lie inside the unit circle in the z plane.

Why are IIR filters not stable?

(a) Stable IIR filter, (b) The same IIR filter becomes unstable due to rounding effects. , one poles lie exactly on the unit circle (ie, it is just out of the region of stability) and hence it is an unstable IIR filter.

Which is the best IIR filter?

The Butterworth filter provides the best Taylor Series approximation to the ideal lowpass filter response at analog frequencies and ; for any order N, the magnitude squared response has 2N-1 zero derivatives at these locations (maximally flat at and ). Response is monotonic overall, decreasing smoothly from to . at .

Which filters are inherently stable?

An FIR filter is a filter with no feedback in its equation. This can be an advantage because it makes an FIR filter inherently stable.