High-Speed Fixed and Floating Point Implementation of Delta-Operator Formulated Discrete Time Systems
Abstract
This report addresses the analysis and design of finite wordlength length implementations of linear t.i.v. delta-systems and the development of a 2-D delta-operator state space model. It is shown that in fixed point arithmetic linear t.i.v. systems implementation in delta-operator form do not generally outperform their q-operator counterpart. In fact, delta-operator systems always show unstable limit cycle behavior and convergence to incorrect equilibrium points, independent of the choice of the realization or the sampling time. The coefficient sensitivity for delta-systems is still superior to the shift- operator. In the case of floating point arithmetic, delta-operator implementations perform consistently better than their shift-operator counterparts. Delta-systems show superior quantization noise and sensitivity properties. The zero-convergence problem of the fixed point case does not exist if the mantissa length is chosen sufficiently large. Due to its attractive finite wordlength properties, the concept of delta-operators has been extended to the multi-dimensional case. A 2-D state space model was developed and the notions of reachability and observability gramian and balanced realization have been introduced. The problem of directly checking stability in the delta-domain has also been addressed. Similarly to the 1-D case, the sensitivity & roundoff noise behavior was analyzed
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 05, 1994
- Accession Number
- ADA283109
Entities
People
- Peter H. Bauer
Organizations
- University of Notre Dame