A practical digital filter is a non linear system caused by the quantification of the arithmetic operations. Such non linear-ties may cause an IIR filter, which is stable under infinite precision, to exhibits an unstable behavior under finite precision arithmetic for specific input signals, such as zero or constant inputs. This type of instability usually results in an oscillatory periodic o/p called a limit cycle.

There are basically two types limit cycles.

1] Granular.

2] Overflow.

Granular Limit Cycle.

Two types of granular limit cycle have been observed in IIR digital filters: Inaccessible and accessible limit cycles. The former type can appear only if the initial conditions of the digital filter at the time of starting pertain to that limit cycle, whereas in the second case, the limits condition can be reached by starting the digital filter with initial conditions not pertaining to the limit cycle.

Overflow.

Limit cycle like oscillations can also result from overflow in digital filters implemented with finite precision arithmetic. The amplitude of the overflow oscillations can cover the whole dynamic range of the register.