Fourier Transforms in Radar and Signal Processing -- Contents v -- Preface xi -- 1 Introduction 1 -- 1.1 Aim of the Work 1 -- 1.2 Origin of the Rules and Pairs Method for Fourier Transforms 2 -- 1.3 Outline of the Rules and Pair Method 3 -- 1.4 The Fourier Transform and Generalized Functions 4 -- 1.5 Complex Waveforms and Spectra in Signal Processing 7 -- 1.6 Outline of the Contents 8 -- References 10 -- 2 Rules and Pairs 11 -- 2.1 Introduction 11 -- 2.2 Notation 12 -- 2.3 Rules and Pairs 21 -- 2.4 Three Illustrations 24 -- Appendix 2A: Properties of the sinc Function 27 -- Appendix 2B: Breif Derivations of the Rules and Pairs 29 -- 3 Pluse Spectra 39 -- 3.1 Introduction 39 -- 3.2 Symmetrical Trapezoidal Pulse 40 -- 3.3 Symmetrical Triangular Pulse 41 -- 3.4 Asymmetrical Trapezoidal Pulse 44 -- 3.5 Raised cosine Pulse 47 -- 3.6 Rounded Pulses 49 -- 3.7 General Rounded Trapezoidal Pulse 53 -- 3.8 Regular Train of Identical RF Pulses 58 -- 3.9 Carrier Gated by a Regular Pulse Train 59 -- 3.10 Pulse Doppler Radar Target Return 61 -- 3.11 Summary 62 -- 4 Sampling Theory 65 -- 4.1 Introduction 65 -- 4.2 Basic Technique 66 -- 4.3 Wideband Sampling 67 -- 4.4 Uniform Sampling 69 -- 4.5 Hilbert Sampling 74 -- 4.6 Quadrature Sampling 75 -- 4.7 Low IF Analytic Signal Sampling 81 -- 4.8 High IF Sampling 84 -- 4.9 Summary 85 -- References 86 -- Appendix 4A: The Hilbert Transform 86 -- 5 Interpolation for Delayed Waveform Time Series 89 -- 5.1 Introduction 89 -- 5.2 Spectrum Independent Interpolation 90 -- 5.3 Least Squared Error Interpolation 107 -- 5.4 Application to Generation of Simulated Gaussian Clutter 114 -- 5.5 Resampling 120 -- 5.6 Summary 122 -- References 123 -- 6 Equalization 125 -- 6.1 Introduction 125 -- 6.2 Basic Approach 126 -- 6.3 ramp and sncr Functions 130 -- 6.4 Simple Example of Amplitude Equalization 134.

6.5 Equalization for Broadband Array Radar 135 -- 6.6 Sum Beam Equalization 138 -- 6.7 Difference Beam Equalization 147 -- 6.8 Summary 158 -- 7 Array Beamforming 161 -- 7.1 Introduction 161 -- 7.2 Basic Principles 162 -- 7.3 Uniform Linear Arrays 164 -- 7.4 Nonuniform Linear Arrays 180 -- 7.5 Summary 187 -- Final Remarks 189 -- About the Author 191 -- Index 193.