High-Speed Fixed and Floating Point Implementation of Delta-Operator Formulated Discrete Time Systems.
Final rept. 1 Jan - 31 Dec 94,
NOTRE DAME UNIV IN DEPT OF ELECTRICAL ENGINEERING
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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 delta-systems, b 2-D and m-D delta system models and c extentions of delta-operators 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 shift-operator case and condItions for superiority of the delta-operator are established. In particular, in the first area it was shown, that delta-operator 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 non-existent in floating point realizations, if the mantissa length is sufficiently high. In the second area b, the 2-D and m-D Roesser model for delta-systems 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, delta-operator 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.
- Theoretical Mathematics