Why recursion amplifies small errors
An IIR filter feeds part of its output back into the next step. Quantization therefore changes not only the current sample, but also the signal that will be reused in later steps.
For a stable design, the pole locations need enough margin that coefficient rounding does not move them across the unit circle.
Practical checks
| Check | Question |
|---|---|
| Coefficients | How many fractional bits are available? |
| Poles | How close are they to the unit circle? |
| Output | Does the error remain bounded over long runs? |
The best first experiment is usually a long constant-input simulation, followed by a sweep over coefficient precision.