Testing Stability of Digital Filters Using Optimization Methods with Phase Analysis

In this paper, novel methods for the evaluation of digital-filter stability are investigated. The based on phase analysis a complex function in characteristic equation digital filter. It allows evaluating when is not polynomial. operation these relies sampling unit circle plane and extracting quadrant value each sample. By calculating function-phase quadrants, regions immediate vicinity unstable roots (i.e., zeros), called candidate regions, determined. both real imaginary parts complex-function values change signs. Then, explored. When sizes reduced below an assumed accuracy, then filter instability verified with use discrete Cauchy’s argument principle. Three different algorithms unit-circle benchmarked, i.e., global poles finding (GRPF) algorithm, multimodal genetic algorithm (MGA-WPA), particle swarm optimization (MPSO-WPA). compared four benchmarks integer- fractional-order filters systems. Each demonstrates slightly properties. GRPF very fast efficient; however, it requires initial number nodes large enough to detect all roots. MPSO-WPA prevents missing due usage stochastic space exploration by subsequent swarms. MGA-WPA converges effectively generating small individuals limiting final population size. conducted research leads conclusion that such as more likely system instability, especially they run multiple times. If computing time vitally important user, right choice, because significantly