Fourier transforms are used everyday for solving single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been solved by using Fourier transforms have gone unsolved because they require integration that is too computationally difficult. This manual demonstrates how you can solve those integration-intensive problems with an approach to carrying out Fourier transforms. By building upon Woodward's well-known "Rules and Pairs" method and related concepts and procedures, the text establishes a unified system that makes implicit the integration required for performing Fourier transforms on a wide variety of functions. It details how complex functions can be broken down to their constituent parts for analysis. This approach to applying Fourier transforms is illustrated with many specific examples from digital signal processing as well as radar and antenna operation.
Author(s): David Brandwood
Series: Artech House Radar Library
Publisher: Artech House Publishers
Year: 2003
Language: English
Pages: 212
Contents......Page 6
Preface......Page 12
1.1 Aim of the Work 1......Page 14
1.2 Origin of the Rules and Pairs Method for Fourier Transforms......Page 15
1.3 Outline of the Rules and Pair Method......Page 16
1.4 The Fourier Transform and Generalized Functions......Page 17
1.5 Complex Waveforms and Spectra in Signal Processing......Page 20
1.6 Outline of the Contents......Page 21
References......Page 23
2.1 Introduction......Page 24
2.2 Notation......Page 25
2.3 Rules and Pairs......Page 34
2.4 Three Illustrations......Page 37
Appendix 2A: Properties of the sinc Function......Page 40
Appendix 2B: Breif Derivations of the Rules and Pairs......Page 42
3.1 Introduction......Page 52
3.2 Symmetrical Trapezoidal Pulse......Page 53
3.3 Symmetrical Triangular Pulse......Page 54
3.4 Asymmetrical Trapezoidal Pulse......Page 57
3.5 Raised cosine Pulse......Page 60
3.6 Rounded Pulses......Page 62
3.7 General Rounded Trapezoidal Pulse......Page 66
3.8 Regular Train of Identical RF Pulses......Page 71
3.9 Carrier Gated by a Regular Pulse Train......Page 72
3.10 Pulse Doppler Radar Target Return......Page 74
3.11 Summary......Page 75
4.1 Introduction......Page 78
4.2 Basic Technique......Page 79
4.3 Wideband Sampling......Page 80
4.4 Uniform Sampling......Page 82
4.5 Hilbert Sampling......Page 87
4.6 Quadrature Sampling......Page 88
4.7 Low IF Analytic Signal Sampling......Page 94
4.8 High IF Sampling......Page 97
4.9 Summary......Page 98
Appendix 4A: The Hilbert Transform......Page 99
5.1 Introduction......Page 102
5.2 Spectrum Independent Interpolation......Page 103
5.3 Least Squared Error Interpolation......Page 120
5.4 Application to Generation of Simulated Gaussian Clutter......Page 127
5.5 Resampling......Page 133
5.6 Summary......Page 135
References......Page 136
6.1 Introduction......Page 138
6.2 Basic Approach......Page 139
6.3 ramp and sncr Functions......Page 143
6.4 Simple Example of Amplitude Equalization......Page 147
6.5 Equalization for Broadband Array Radar......Page 148
6.6 Sum Beam Equalization......Page 151
6.7 Difference Beam Equalization......Page 160
6.8 Summary......Page 171
7.1 Introduction......Page 174
7.2 Basic Principles......Page 175
7.3 Uniform Linear Arrays......Page 177
7.4 Nonuniform Linear Arrays......Page 193
7.5 Summary......Page 200
Final Remarks......Page 202
About the Author......Page 204
Index 193......Page 206
