TABLE OF CONTENTS Transforms have been used in a number of chapters:
Chapter 2, Usual and unusual concepts, introduced the method of illustrating complex functions and their Fourier transforms used in this book.
In Chapter 3, Transmitters, Fourier transforms were used to calculate transmitter spectra with and without pulse compression.
Chapter 5, Antennas, used Fourier and Hankel transforms to calculate antenna patterns, and inverse Fourier transforms to calculate the illumination function for a specified pattern.
Chapter 8, Matched and matching filters, showed the use of inverse Fourier transforms to calculate the shape of filtered pulses, with and without pulse compression.
Chapter 11, Signal processing, showed the use of Fourier and z transforms for calculating the effects of signal processing in the frequency and time domains.
Chapter 12, Threshold and detection, used Fourier transforms to add the probability distributions of signals and noise.
Chapter 15, Statistics, employed Fourier transforms to find the statistical sums of probability distributions.
Common aspects of the use of transforms in this book are discussed in this chapter, and full mathematical descriptions are to be found in textbooks, examples are [1 3]. The notation used in this book is shown in Table 16.1.
| Basic function | Transformed function | ||
|---|---|---|---|
| Symbol | Function | Symbol | Function |
| h( t) | Time function | H( p) | Laplace transform |
| H( ?) | Fourier transform, ? convention | ||
| H( f) | Fourier transform, f convention | ||
| H( z) | z |
