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# Fourier Transforms in Radar and Signal Processing

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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. Now you can solve many of these problems with the integration-free approach to carrying out Fourier transforms (and Fourier series) presented in this book.

By building upon Woodward’s well known “Rules and Pairs” 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 new approach to applying Fourier transforms is illustrated with many specific examples from digital signal processing as well as radar and antenna operation.

Contents:

Introduction - Aim of the Work. Origin of the Rules and Pairs Method for Fourier Transforms. Outline of the Rules and Pairs Method. The Fourier Transform and Generalized Functions. Complex Waveforms and Spectra in Signal Processing. Outline of the Contents.

Rules and Pairs - Introduction. Notation. Rules and Pairs. Three Illustrations. Properties of the sinc Function. Brief Derivations of the Rules and Pairs.

Pulse Spectra - Introduction. Symmetrical Trapezoidal Pulse. Symmetrical Triangular Pulse. Asymmetrical Trapezoidal Pulse. Raised cosine Pulse. Rounded Pulses. General Rounded Trapezoidal Pulse. Regular Train of Identical RF Pulses. Carrier Gated by a Regular Pulse Train. Pulse Doppler Radar Target Return. Summary.

Sampling Theory - Introduction. Basic Method. Wideband Sampling. Uniform Sampling. Hilbert Sampling. Quadrate Sampling. Low IF Analytic Signal Sampling. High IF Sampling. Summary. The Hilbert Transform.

Interpolation For Delayed Waveform Time Series - Introduction. Spectrum Independent Interpolation. Least Squared Error Interpolation. Application to Generation of Simulated Gaussian Clutter. Resampling. Summary.

Equalization - Introduction. Basic Approach. ramp and sncr Functions. Simple Example of Amplitude Equalization. Equalization for Broadband Array Radar. Sum Beam Equalization. Summary.

Array Beamforming - Introduction. Basic Principles. Uniform Linear Arrays. Nonuniform Linear Arrays. Summary.

David Brandwood is a senior consultant at Roke Manor Research located in Romsey, Hants, U.K. A contributor to IEE conferences and journals, he holds one degree in physics from Oxford University and another in mathematics from the Open University.

Artech House; February 2003
211 pages; ISBN 9781580536134