Numerical Stability

Introduction Most DSP filter designs fail not in theory — but in embedded deployment. Fixed-point systems introduce: quantization overflow feedback amplification limit cycles Without explicit engineering safeguards, instability is inevitable. Why Floating-Point Designs Break in Fixed-Point Hardware Key failure modes: coefficient truncation reduced dynamic range nonlinear saturation feedback noise growth IIR structures are especially vulnerable. Scaling as a First-Class Design Variable Proper deployment requires: per-section scaling headroom budgeting bounded internal states Blind normalization is insufficient. ...

Introduction Modern DSP tools increasingly rely on automated optimization to design filters. By minimizing spectral error or maximizing attenuation, algorithms attempt to generate “optimal” responses. In practice, these filters frequently fail after deployment. Common symptoms include instability, excessive distortion, numerical fragility, and unpredictable behavior across operating conditions. This article explains why blind optimization fails in real DSP systems and why engineering constraints are essential for deployable design. Optimization Ignores Physical and Numerical Limits Most optimization algorithms treat filter coefficients as continuous variables. ...