TABLE OF CONTENTS This appendix treats tapering functions and their Fourier transforms in a common way irrespective of their usual use for antenna patterns or signal processing. The tapering functions in this chapter are grouped into:
| Transmitter pulse shaping, antenna patterns, and filtering; |
| Circular antennas; |
| Monopulse antennas. Odd functions are also used for differentiating filters which are not covered in this book. |
The notation used follows [1].
This appendix shows functions limited in distance, time, or bandwidth and their Fourier transforms. In order to be able to show these for all the tapering functions for all circumstances, they must be normalized to unit width. In order to present the parameters and results in a unified form, the variables p' and q' are used. Thus:
| h( p) | transforms to | H( q) and |
| h( P') | transforms to | H( q'), with normized variables |
The conventions for describing limited distance, time, and bandwidth functions are shown in Table B.1.
| ANTENNA | WAVEFORM | SPECTRUM | ||
|---|---|---|---|---|
| Linear | Circular | |||
| Width | w, m | D, m | ?, s | B, Hz |
| Width limits |
 |
 |
 |
 |
| p | x, m | r, m | t, s | f, Hz |
| p' |
 |
 |
 |
 |
| Functions | g( x), g( x') | g( r), g( r) | h( t), h( t') | H( f), |
