TABLE OF CONTENTS In Chapter 12, Threshold and detection, a number of statistical distributions are used, some of which are related. In the past, before the personal calculator or the computer age, distributions had to be chosen for which there were tables of the values. This text is not a mathematical treatment but an introduction to the families of distributions and their relationships. References [1 3] furnish the theory behind this chapter.
There are many more statistical distributions than those described in this chapter, and only those mentioned in other chapters are discussed. Discrete distributions, for example, the Poisson distribution, which do not have any use in antenna theory or signal processing, are omitted.
This chapter also introduces the Fourier transforms, or characteristic functions, of statistical probability distribution functions. The discussion is limited to the requirements of this book and the reader is referred to statistical texts for a more fundamental treatment. In contrast to statistical texts that use the + ? convention for their Fourier transforms, the - f convention is used here to be compatible with other radar tests [4]. The sense of the loops representing characteristic functions is the reverse of those in [5, Chapter 6] and there is a factor of 2 ? in the scaling of the ? axis.
Fourier transforms for for spectra and antenna diagrams are discussed in Chapter 16.
A number of terms are used to describe the sizes and shapes of the distributions illustrated in Figure 15.1. A...
