Embedded DSP

Introduction Digital filter design is often taught as an optimization problem. Given a desired frequency response, algorithms compute filter coefficients that approximate that response. In real engineering systems, however, filter design is rarely that simple. Engineers must consider multiple constraints simultaneously: numerical precision computational cost signal distortion limits drift tolerance stability margins Ignoring these constraints leads to filters that work in theory but fail in production. This article explains why constraint-driven filter design is essential for practical DSP systems. ...

Introduction Notch filters are commonly used to remove narrowband interference from signals. Typical applications include removing mains hum, switching noise, or mechanical vibration tones. In theory, designing a notch filter is straightforward. Once the interference frequency is known, a filter can be placed precisely at that frequency. However, in real engineering systems notch filters often perform poorly. The filter may fail to remove the interference, distort nearby signals, or even introduce numerical instability. ...

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. ...