A Deterministic Analysis of Limit Cycle Oscillations in Recursive Digital Filters due to Quantization

摘要

A deterministic analysis of the limit cycle oscillations which occur in fixed-point implementations of recursive digital filters due to roundoff and truncation quantization after multiplication operations, is performed. Amplitude bounds, based upon a correlated nonstochastic signal approach and Lyapunov's direct method, as well as an approximate expression for the frequency of zero-input limit cycles, are derived and tested for the two-pole filter. The limit cycles are represented on a successive value phase-plane diagram from which certain symmetry properties are derived. Similar results are developed for other second-order digital filter configurations, and the parallel and cascade forms. The results are extended to include limit cycles under input signal conditions. A basic design relationship between the number of significant digits required for the realization of a filter algorithm with a desired signal-to-noise (limit cycle) ratio is stated.