High-Speed Fixed- and Floating-Point Implementation of Delta-Operator Formulated Discrete-Time Systems.
Abstract
This report addresses the analysis and design of finite word- length implementations of linear time-invariant delta-operator formulated discrete-time systems and the development of a 2-D delta-operator state-space model. It is shown that, in fixed-point arithmetic, linear time-invariant systems implemented with delta- operator do not generally outperform their shift-operator counterparts; they always show unstable limit cycle behavior and convergence to incorrect equilibria independent of realization and sampling time. Coefficient sensitivity is still superior. With floating-point arithmetic, delta-operator implementations consistently perform better than their shift-operator counterparts. They show superior quantization noise and sensitivity properties. Zero convergence problem of the fixed-point case does not exist if the mantissa length is sufficiently large. Noting these attractive finite wordlength properties, the concept of delta-operator has been extended to the multi-dimensional case. A 2-D state-space model, the notions of gramians, and balanced realization have been introduced. As for the 1-D case, sensitivity and roundoff noise behavior was analyzed. Realiviza tion that 1-D case, sensitivity are equivalent to balanced realizations. The problem of directly checking stability in the delta-domain has also been addressed. (AN)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 03, 1994
- Accession Number
- ADA298948
Entities
People
- Kamal Premaratne
- Peter H. Bauer
Organizations
- University of Miami