Limit Cycles in IIR Filters: Hidden Instability in Fixed-Point DSP Systems
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. ...