
Accession Number : ADA301060
Title : HighSpeed Fixed and Floating Point Implementation of DeltaOperator Formulated Discrete Time Systems.
Descriptive Note : Final rept. 1 Jan  31 Dec 94,
Corporate Author : NOTRE DAME UNIV IN DEPT OF ELECTRICAL ENGINEERING
Personal Author(s) : Bauer, Peter H.
PDF Url : ADA301060
Report Date : 24 FEB 1995
Pagination or Media Count : 252
Abstract : This final report describes research results on flnite wordlength implementations of delta operator based discrete systems. It addresses three distinct problems: (a) the existence of limit cycles in fixed and floating point deltasystems, (b) 2D and mD delta system models and (c) extentions of deltaoperators to the nonlinear case. All studies in the above three main areas are of comparative nature, i.e. the results are compared with the known results for the shiftoperator case and condItions for superiority of the deltaoperator are established. In particular, in the first area it was shown, that deltaoperator based fixed point designs cannot be free of limit cycles, regardless of the quantization format. It was also shown, that the limit cycle problem is virtually nonexistent in floating point realizations, if the mantissa length is sufficiently high. In the second area (b), the 2D and mD Roesser model for deltasystems were developed and analyzed. The notions of reachability and observability gramians as well as the notion of balanced realization were introduced and the sensitivity and roundoff noise behavior analyzed. Finally in the third area (c), deltaoperator representations of nonlinear systems were developed and analyzed. Sensitivity measure of the state trajectory were developed and evaluated. Quantization error bounds in delta systems were derived for certain classes of nonlinear functions.
Descriptors : *OPERATORS(MATHEMATICS), *FLOATING POINT OPERATION, MEASUREMENT, STABILITY, CHAOS, SENSITIVITY, CYCLES, TIME, NONLINEAR SYSTEMS, ERRORS, FORMATS, QUANTIZATION, DIFFERENTIAL EQUATIONS, BEHAVIOR, NOISE, TRAJECTORIES, FUNCTIONS(MATHEMATICS).
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE