I am studying IIR filters read about limit-cycle oscillations in IIR filters. From what I understand, there are two types of oscillations
- Granularity limit-cycle: when signal levels become very low or constant for a period of time, the filter can lock into unstable modes and generate low-level output oscillations. This is caused by quantization errors.
- Overflow limit-cycle: oscillations can appear (as large as the maximum signal range) due to overflow.
Knowing the transfer function of the IIR filter, is there any way to predict if these errors can occur knowing the coefficients of my filter? My guess is that this has to do with the denominator coefficients since this behaviour is exclusiveto IIR filters and not FIR filters. Can someone please help me? Thank you!
An example I came across with
$$a_0=a_2=0.00118011$$ $$a_1=-0.00155979$$ $$b_1=1.95961$$ $$b_2=-0.960411$$
It is justified that this filter suffers from limit-cycle overflow because:
It is said the there is an alternate output.