Fourier Transforms in Radar and Signal Processing Second Edition -- Contents -- Preface -- Preface to the First Edition -- 1 Introduction -- 1.1 Aim of the Work -- 1.2 Origin of the Rules-and-Pairs Method for Fourier Transforms -- 1.3 Outline of the Rules-and-Pairs Method -- 1.4 The Fourier Transform and Generalized Functions -- 1.5 Complex Waveforms and Spectra in Signal Processing -- 1.6 Outline of the Contents -- References -- 2 Rules and Pairs -- 2.1 Introduction -- 2.2 Notation -- 2.2.1 Fourier Transform and Inverse Fourier Transform -- 2.2.2 rect and sinc -- 2.2.3 d-function and Step Function -- 2.2.4 rep and comb -- 2.2.5 Convolution -- 2.3 Rules and Pairs -- 2.4 Four Illustrations -- 2.4.1 Narrowband Waveforms -- 2.4.2 Parseval's Theorem -- 2.4.3 The Wiener-Khinchine Relation -- 2.4.4 Sum of Shifted sinc Functions -- Appendix 2B: Brief Derivations of the Rules and Pairs -- 2B.1 Rules -- 2B.2 Pairs -- 3 Pulse Spectra -- 3.1 Introduction -- 3.2 Symmetrical Trapezoidal Pulse -- 3.3 Symmetrical Triangular Pulse -- 3.4 Asymmetric Trapezoidal Pulse -- 3.5 Asymmetric Triangular Pulse -- 3.6 Raised Cosine Pulse -- 3.7 Rounded Pulses -- 3.8 General Rounded Trapezoidal Pulse -- 3.9 Regular Train of Identical RF Pulses -- 3.10 Carrier Gated by a Regular Pulse Train -- 3.11 Pulse Doppler Radar Target Return -- 3.12 Summary -- 4 Periodic Waveforms, Fourier Series,and Discrete Fourier Transforms -- 4.1 Introduction -- 4.2 Power Relations for Periodic Waveforms -- 4.2.1 Energy and Power -- 4.2.2 Power in the d -Function -- 4.2.3 General Periodic Function -- 4.2.4 Regularly Sampled Function -- 4.2.5 Note on Dimensions -- 4.3 Fourier Series of Real Functions Using Rules and Pairs -- 4.3.1 Fourier Series Coefficients -- 4.3.2 Fourier Series of Square Wave -- 4.3.3 Fourier Series of Sawtooth -- 4.3.4 Fourier Series of Triangular Waves.

4.3.5 Fourier Series of Rectified Sinewaves -- 4.4 Discrete Fourier Transforms -- 4.4.1 General Discrete Waveform -- 4.4.2 Transform of Regular Time Series -- 4.4.3 Transform of Sampled Periodic Spectrum -- 4.4.4 Fast Fourier Transform -- 4.4.5 Examples Illustrating the FFT and DFT -- 4.4.6 Matrix Representation of DFT -- 4.4.7 Efficient Convolution Using the FFT -- 4.5 Summary -- Appendix 4A: Spectrum of Time-Limited Waveform -- Appendix 4B: Constraint on Repetition Period -- 5 Sampling Theory -- 5.1 Introduction -- 5.2 Basic Technique -- 5.3 Wideband Sampling -- 5.4 Uniform Sampling -- 5.4.1 Minimum Sampling Rate -- 5.4.2 General Sampling Rate -- 5.5 Hilbert Sampling -- 5.6 Quadrature Sampling -- 5.6.1 Basic Analysis -- 5.6.2 General Sampling Rate -- 5.7 Low IF Analytic Signal Sampling -- 5.8 High IF Sampling -- 5.9 Summary -- References -- Appendix 5A: The Hilbert Transform -- 6 Interpolation for Delayed WaveformTime Series -- 6.1 Introduction -- 6.2 Spectrum Independent Interpolation -- 6.2.1 Minimum Sampling Rate Solution -- 6.2.2 Oversampling and the Spectral Gating Condition -- 6.2.3 Three Spectral Gates -- 6.2.4 Results and Comparisons -- 6.3 Least Squared Error Interpolation -- 6.3.1 Method of Minimum Residual Error Power -- 6.3.2 Power Spectra and Autocorrelation Functions -- 6.3.3 Error Power Levels -- 6.4 Application to Generation of Simulated Gaussian Clutter -- 6.4.1 Direct Generation of Gaussian Clutter Waveform -- 6.4.2 Efficient Clutter Waveform Generation, Using Interpolation -- 6.5 Resampling -- 6.6 Summary -- References -- 7 Equalization -- 7.1 Introduction -- 7.2 Basic Approach -- 7.3 ramp and sncr Functions -- 7.4 Example of Amplitude Equalization -- 7.5 Equalization for Broadband Array Radar -- 7.6 Sum Beam Equalization -- 7.7 Difference Beam Equalization -- 7.8 Summary -- 8 Array Beamforming -- 8.1 Introduction.

8.2 Basic Principles -- 8.3 Uniform Linear Arrays -- 8.3.1 Directional Beams -- 8.3.2 Low Sidelobe Patterns -- 8.3.3 Sector Beams -- 8.4 Nonuniform Linear Arrays -- 8.4.1 Prescribed Patterns from Nonuniform Linear Arrays -- 8.4.2 Sector Beams from a Nonuniform Linear Array -- 8.5 Summary -- Final Remarks -- About the Author -- Index.