High-Speed Fixed- and Floating-Point Implementation of Delta-Operator FormulatedDiscrete-Time Systems

摘要

This final report addresses research; results on three areas (a) Analysis andDesign of Finite Wordlength Implementations of Linear, Time-Invariant Delta-Systems: With fixed-point, delta-operator based implementations are shown to always possess limit cycles regardless of quantization format. This problem is virtually non-existent with floating-point if mantissa is sufficiently long. When this is the case, delta-systems offer superior performance (especially, for sampled continuous-time systems) with high sampling rate. (b) Analysis of Nonlinear Circuits Through Delta-Operator Based Schemes: Delta-operator based numerical schemes for nonlinear system simulation were proposed. For certain classes of nonlinearities, sensitivity measures and quantization error bounds for state orbit were also developed. With floating-point, the proposed numerical schemes are shown to produce superior performance when using a small discretization step size. (c) 2-D and m-D Delta-Models: Delta-models for 2-D and m-D discrete-time systems were developed. Notions of gramians, balanced realizations, etc., were introduced, Coefficient sensitivity was also analyzed. Ml results obtained were compared with corresponding results for the shift-operator case. Conditions where delta-systems are superior are also established.