Zero input behavior of fixed-point digital filters in delta-operator representation

This paper analyzes the zero input behavior of digital filters in delta-operator representation. It is shown that regardless of the quantization and precision scheme, delta-operator based digital filters show very poor zero-convergence. Under zero input conditions the state trajectory typically terminates in a non-zero equilibrium point. The geometry of the arising deadbands are derived and lower as well as upper bounds on the limit cycle amplitudes are obtained. The analysis is conducted in the state space and is independent of the form of the system matrix. The result applies to all commonly used arithmetic schemes and precision options.