This book is all about finite wordlength errors in digital filters, con trollers and estimators, and how to minimize the deleterious effects of these errors on the performance of these devices. This does by no means imply that all about finite wordlength errors in filters, controllers and estimators is to be found in this book. We first ventured into the world of finite wordlength effects in 1987 when Gang Li began his PhD thesis in this area. Our more experienced readers might well say 'This shows', but we believe that the extent of our new contributions largely offsets our relative inexperience about the subject that might surface here and there in the book. Our naive view on the subject of finite wordlength errors in 1987 could probably be summarized as follows: • numerical errors due to finite wordlength encoding and roundoff are something that one has to live with, and there is probably not much that can be done about them except to increase the wordlength by improvements on the hardware; • these errors are as old as finite arithmetic and numerical analysis and they must therefore be well understood by now; • thus, if something can be done to minimize their effects, it must have been analysed and put into practice a long time ago. It is almost fair to say that we were wrong on all counts. The subject of this publication is the minimization of the effects of numerical errors on the performance of digital filters, controllers and adaptive parameter estimators. This minimization is achieved through the use of optimal implementations. The computation of such optimal implementations, which minimise various measures of performance degradation, forms the main part of the book. The novelty is in the wide range of performance criteria, which reflects a range of application areas, and in the computation of the optimal solutions. A typical chapter consists of a problem formulation giving the choice of a performance measure. This is discussed in its relevance and expression in terms of the set of possible realizations, and its minimization. Front Matter....Pages i-xv Introduction....Pages 1-21 Finite Word Length errors and computations....Pages 23-44 Parametrizations in digital system design....Pages 45-83 Frequency weighted optimal design....Pages 85-107 A new transfer function sensitivity measure....Pages 109-125 Pole and zero sensitivity minimization....Pages 127-158 A synthetic sensitivity — roundoff design....Pages 159-181 Sparse optimal and suboptimal realizations....Pages 183-215 Parametrizations in control problems....Pages 217-259 Synthetic FWL compensator design....Pages 261-287 Parametrizations in the Delta operator....Pages 289-318 Generalized transfer function parametrizations for adaptive estimation....Pages 319-358 Back Matter....Pages 359-373 Contents: Introduction Finite Word Length and Computations Parametrizations in Digital System Design Frequency Weighted Optimal Design New Transfer Function Sensitivity Measure Pole and Zero Sensitivity Minimization Synthetic Sensitivity-Roundoff Design Sparse Optimal and Suboptimal Realizations Parametrizations in Control Problems Synthetic FWL Compensator Design Parametrizations in the Delta Operator Generalised Transfer Function Parametrizations for Adaptive Estimation.
