• Introduction.- The Image Plane.- Two-dimensional Impulse Functions.- The Two-dimensional Fourier Transform.- Two-dimensional Convolution.- The Two-dimensional Convolution Theorem.- Sampling and Interpolation in Two Dimensions.- Digital Operations.- Rotational Symmetry.- Imaging by Convolution.- Diffraction Theory of Sensors and Radiators.- Aperture Synthesis and Interferometry.- Restoration.- The Projection-slice Thoerem.- Computed Tomography.- Synthetic-aperature Radar.- Two-dimensional Noise Images.- Appendix A. Solutions to Problems.- Index.
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As Lord Kelvin said, "Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics." This has remained durable knowledge for a century, and has extended its applicability to topics as diverse as medical imaging (CT scanning), the presentation of images on screens and their digital transmission, remote sensing, geophysical exploration, and many branches of engineering. "Fourier Analysis and Imaging" is based on years of teaching a course on the Fourier Transform at the senior or early graduate level, as well as on Prof. Bracewell's 1995 text "Two-Dimensional Imaging". It is an excellent textbook and will also be a welcome addition to the reference library of those many professionals whose daily activities involve Fourier analysis in its many guises.
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• 1 Introduction 2 Groundwork 3 Convolution 4 Notation for Some Useful Functions 5 The Impulse Symbol 6 The Basic Theorems 7 Obtaining Transforms 8 The Two Domains 9 Waveforms, Spectra, Filters and Linearity 10 Sampling and Series 11 The Discrete Fourier Transform and the FFT 12 The Discrete Hartley Transform 13 Relatives of the Fourier Transform 14 The Laplace Transform 15 Antennas and Optics 16 Applications in Statistics 17 Random Waveforms and Noise 18 Heat Conduction and Diffusion 19 Dynamic Power Spectra 20 Tables of sinc x, sinc2x, and exp(-71x2) 21 Solutions to Selected Problems 22 Pictorial Dictionary of Fourier Transforms 23 The Life of Joseph Fourier.
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This text is designed for use in a senior undergraduate or graduate level course in Fourier Transforms. This text differs from many other Fourier transform books in its emphasis on applications. Bracewell applies mathematical concepts to the physical world throughout this text, equipping students to think about the world and physics in terms of transforms. The pedagogy in this classic text is excellent. The author has included such tools as the pictorial dictionary of transforms and bibliographic references. In addition, there are many excellent problems throughout this book, which are more than mathematical exercises, often requiring students to think in terms of specific situations or asking for educated opinions. To aid students further, discussions of many of the problems can be found at the end of the book.
(source: Nielsen Book Data)

• 1. Introduction.
• 2. The Image Plane.
• 3. Two Dimensional Impulses.
• 4. The Two Dimensional Fourier Transform.
• 5. Two Dimensional Convolution.
• 6. The Convolution Theorem.
• 7. Sampling and Interpolation in Two Dimensions.
• 8. Digital Operations.
• 9. Rotational Symmetry and the Two Dimensional Fourier Transform.
• 10. Imaging by Convolution.
• 11. Diffraction Theory of Sensors.
• 12. Indirect Imaging and Interferometry.
• 13. Restoration of Images.
• 14. The Projection-Slice Theorem.
• 15. Computed Tomography.
• 16. Synthetic Aperture Radar.
• 17. Random Images and Fractals. Index.
• (source: Nielsen Book Data)

• The image plane-- the dimensional impulses-- the two dimensional fourier transform-- two dimensional convolution-- the convolution theorem-- sampling and interpolation in two dimensions-- digital operations-- rotational symmetry and the two dimensional fourier transform-- imaging by convolution-- diffraction theory of sensors-- indirect imaging and interferometry-- restoration of images-- the projection-slice theorem-- computed tornography-- synthetic aperture radar-- random images and fractals.
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Exploring the idea that a two-dimensional image is much the same as a mathematical function of two variables, this study considers a variety of phenomena that are susceptible to mathematical reasoning. It examines the quantitative phenomena that have a wide application in either continuous or discrete situations and discusses specific images associated with techniques such as diffraction, tomography, inferometry and range-Doppler mapping. The book should be accessible to those with mathematical backgrounds but requires no previous experience with transform methods.
(source: Nielsen Book Data)

The author describes the fast algorithm he discovered for spectral analysis and indeed any purpose to which Fourier Transforms and the Fast Fourier Transform are normally applied.
(source: Nielsen Book Data)