Limit Cycles

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. ...

Introduction “Stability” in DSP is not a single concept. A filter can be: mathematically stable on paper numerically unstable after quantization system-unstable when integrated into a control loop regression-unstable when small changes produce different outputs This pillar provides an embedded, production-oriented framework for stability: define stability layers understand dominant failure modes in IIR understand fixed-point-specific pathologies choose FIR vs IIR with engineering constraints validate stability quantitatively The Three Layers of Stability 1) Mathematical Stability Classic definition: poles inside the unit circle. ...