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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.
Transform methods provide a unifying mathematical approach to the study of electrical networks, devices for energy conversion and control, antennas, and other components of electrical systems, as well as to complete linear systems and to many other physical systems and devices, whether electrical or not. These same methods apply equally to the subjects of electrical communication by wire or optical fiber, to wireless radio propagation, and to ionized media — which are all concerned with the interconnection of electrical systems — and to information theory which, among other things, relates to the acquisition, processing, and presentation of data. Other theoretical techniques are used in handling these basic fields of electrical engineering, but transform methods are virtually indispensable in all of them. Fourier analysis as applied to electrical engineering is sufficiently important to have earned a permanent place in the curriculum — indeed much of the mathematical development took place in connection with alternating current theory, signal analysis, and information theory as formulated in connection with electrical communication.
This is why much of the literature dealing with technical applications has appeared in electrical and electronic journals. Despite the strong bonds with electrical engineering, Fourier analysis nevertheless has become indispensable in bio-medicine and remote sensing (geophysics, oceanography, planetary surfaces, civil engineering), where practitioners now outnumber those electrical engineers who regularly use Fourier analysis. But the teaching of Fourier analysis and its applications still finds its home in electrical engineering