IIR Filter check for limit-cycle oscilations

1. How do you prevent limit cycle oscillations?
2. What is limit cycle oscillation?
3. How do I know if my IIR filter is stable?
4. Which filter is free of limit cycle oscillations when implemented on a finite word length digital system?

How do you prevent limit cycle oscillations?

One is to determine a bound on the maximum limit cycle amplitude, expressed as an integral number of quantization steps [13]. It is then possible to choose a word length that makes the limit cycle amplitude acceptably low. Alternately, limit cycles can be prevented by randomly rounding calculations up or down [14].

What is limit cycle oscillation?

Limit cycle is an oscillation peculiar to nonlinear systems. The oscillatory behavior, unexplainable in terms of linear theory, is characterized by a constant amplitude and frequency determined by the nonlinear properties of the system.

How do I know if my IIR filter is 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.

Which filter is free of limit cycle oscillations when implemented on a finite word length digital system?

Non-recursive FIR filters don't experience limit cycle oscillations. Technically, in a practical, stable IIR filter excited by a finite sequence, the output will eventually decay to zero. But due to the non-linearities in the system, the issue of the limit cycle will keep some oscillations going in the output.