Limit-cycle oscillations in digital filters

A deterministic analysis of limit-cycle oscillations, which occur in fixed-point implementations of recursive digital filters due to roundoff and truncation quantization after multiplication, is performed. Amplitude bounds, based upon a correlated (nonstochastic) signal approach using Lyapunov´s direct method, as well as a general matrix formulation for zero-input limit cycles, are derived and tested for the two-pole filter. The limit cycles are represented on a successive-value phase-plane-type diagram from which certain symmetry properties are derived. The results are extended to include limit cycles under input-signal conditions.