Fourier Transforms in Radar and Signal Processing (Artech House Radar Library (Hardcover))

✍ Scribed by David Brandwood

• Publisher: Artech House
• Year: 2011
• Tongue: English
• Leaves: 279
• Edition: 2
• Category: Library

✦ Synopsis

Electrical engineers working in radar, sonar, and signal processing use Fourier transform relationships everyday on the job. This book presents a coordinated system for performing Fourier transforms on a variety of functions. It illustrates how to apply Fourier transforms to many specific examples in radar, signal processing, and antenna design.

✦ Table of Contents

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