Title :
New limit cycle bounds for digital filters
Author :
Green, B.D. ; Turner, L.E.
Author_Institution :
Dept. of Electr. Eng., Calgary Univ., Alta., Canada
fDate :
4/1/1988 12:00:00 AM
Abstract :
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
Keywords :
band-pass filters; digital filters; filtering and prediction theory; limit cycles; low-pass filters; Chebyshev magnitude response characteristics; arbitrary order; constant-input limit cycles; digital filters; elliptic-bandpass-filter; fifth-order; fixed point filters; geometric interpretation; higher-order sections; limit cycle bounds; low-pass filters; nonlinearity; period-independent bound; reduced bound; second-order sections; sign-magnitude signal quantization; sixth-order; zero-input limit cycles; Algorithm design and analysis; Asymptotic stability; Band pass filters; Delay; Digital filters; Eigenvalues and eigenfunctions; Filtering theory; Limit-cycles; Lyapunov method; Quantization;
Journal_Title :
Circuits and Systems, IEEE Transactions on