New limit cycle bounds for digital filters

A period-independent bound, for zero and constant-input limit cycles in fixed-point digital filters, is developed. The bound is applicable to systems of arbitrary order, provided that all nonideal operations can be consolidated as single nonlinear operations applied at the input to each delay element. Three common types of nonlinearity (i.e. signal quantization) are considered, and a geometric interpretation is used to substantially tighten the bound for sign-magnitude signal quantization. Analytic expressions for the reduced bound are obtained for second-order sections, and an algorithm for computing the bound is presented for higher-order sections. Several numerical examples are presented for second-order sections and compared with previously published results. Two fifth-order low-pass filters (with elliptic and Chebyshev magnitude response characteristics, respectively) and one sixth-order elliptic-bandpass-filter are considered and shown to be free of zero-input limit cycles of amplitude greater than 33