Numerical Precision

Introduction FIR and IIR filters both appear stable in textbook theory. In embedded DSP systems, their real-world behavior can be dramatically different. Engineers frequently discover that designs which simulate perfectly become unstable, noisy, or fragile once deployed. This article explains the practical stability differences between FIR and IIR filters under real numerical constraints. Theoretical Stability vs Practical Stability Mathematically: FIR filters are always stable IIR filters are stable if poles remain inside the unit circle Numerically: ...

Introduction Modern DSP tools can generate filters that look mathematically perfect: razor-sharp notches extreme stopband attenuation minimal theoretical error In simulation, these designs often appear ideal. In production systems, they frequently become unstable, fragile, or harmful. This article explains why over-optimized DSP filters break in real-world deployments and how engineering-grade design avoids these failures. The Optimization Mindset Most automated design tools aim to: minimize spectral error maximize attenuation push constraints to their limits The result is often: ...

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 IIR notch filters are widely used to suppress narrowband interference due to their efficiency and sharp frequency selectivity. However, engineers frequently encounter instability when pushing notch bandwidths extremely narrow—commonly referred to as high-Q designs. Symptoms include: unexpected oscillations amplification instead of attenuation drifting frequency response sensitivity to coefficient quantization This article explains the physical and numerical reasons behind high-Q notch instability and outlines deterministic design practices that prevent it. ...