Introduction

In fixed-point DSP systems, IIR filters may exhibit persistent oscillations even when the input signal is zero.

This phenomenon, known as a limit cycle, is caused by finite word-length effects and nonlinear quantization behavior.

Unlike floating-point simulations, fixed-point arithmetic introduces rounding and saturation effects that can sustain artificial oscillations indefinitely.

Why Limit Cycles Occur

In IIR structures:

  • feedback paths amplify quantization error
  • rounding behaves nonlinearly
  • zero-input does not guarantee zero-output

Small residual quantization noise becomes trapped in feedback loops.

Types of Limit Cycles

Engineers typically encounter:

  • zero-input limit cycles
  • overflow-induced oscillations
  • persistent rounding feedback

These behaviors are invisible in ideal floating-point models.

Mitigation Strategies

Robust design includes:

  • scaling normalization
  • pole-radius margin enforcement
  • dithering techniques
  • post-quantization stability testing

For fixed-point robustness philosophy, see: Fixed-Point DSP Filter Design: Why Floating-Point Stability Does Not Guarantee Deployment Stability

Engineering Takeaway

Limit cycles are not rare bugs.

They are predictable consequences of finite precision arithmetic in feedback systems.

Design must explicitly account for them.

Back to Stability Pillar: Embedded DSP Filter Stability

Conclusion

Ignoring limit cycles leads to unstable embedded behavior.

Deterministic stability margins and quantization-aware design eliminate these hidden failures.