IIR Stability

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. ...

Introduction Digital signal processing textbooks present filter design as a clean mathematical exercise. In real engineering systems, however, filtering is almost never about finding a theoretically optimal response. Engineers must work under strict constraints: limited computational complexity bounded numerical precision phase and latency requirements stability margins regulatory or system-level specifications In practice, most DSP filtering is performed through iterative trial-and-error: inspect spectra, tweak parameters, re-run simulations, and hope the result behaves in deployment. ...