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Fourier Analysis and Imaging
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.
The Fourier Transform and Its Applications
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.
Two-dimensional Imaging
Telecommunication by radio shrank the world to a global village, and the satellite and computer have made imagery the language of that village. The creation of images was once mainly in the hands of artists and scribes. Two-dimensional images also occur naturally: a shadow, the dappled light pattern under a tree, the optical image on a retina. Nature provided the motif for much abstract ornamentation, and our written letters and ideograms trace back to representations of nature.
The Hartly Transform
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The Hartley Transform
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.
