Fourier Transforms in Radar and Signal Processing, Second Edition
1st Edition
Published on 1. January 2011
262 pages
978-1-60807-198-2 (ISBN)
Description
Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a critical new chapter on periodic waveforms - a topic not covered in any other book - and detailed coverage of asymmetric triangular pulse. By building upon Woodward's well known "e;Rules and Pairs"e; method and related concepts and procedures, this book 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. You can now concentrate on functional relationships instead of getting bogged down in the details of integration. This approach to implementing Fourier transforms is illustrated with many specific examples from digital signal processing as well as radar and antenna operation. DVD-ROM Included! Contains MATLAB programs that implement many of the results presented in the book.
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12/2011
Artech House Publishers
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Content
- Intro
- 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
