Error Mechanisms, Filter Structure, and the Sampling Interval

Abstract

This chapter is different in kind from those that have gone before: much of the material is not to be found in other books, and even research journals are not very helpful. It has nevertheless been felt necessary to include such material in this volume because it is of fundamental concern, and as such should be discussed. This entails introducing a number of topics that are still subject to close research but which can nevertheless be described meaningfully in broad terms. As a consequence, mathematical expressions for certain quantities of interest are quoted here and there without deriving them; the derivations, it is felt, are rather intricate considering the nature and objectives of the book, but the expressions are seen to be quite tractable and lend themselves readily to computer implementation. Appropriate references are given, of course, for those who wish to learn more. Presenting the reader with underived mathematical results is a practice we have adopted as seldom as possible, but it was felt that to present the derivations as well as the results would be a large undertaking of dubious value in the circumstances; we can only hope that our judgement in the matter has been correct.