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Fourier Techniques and Applications (Paperback, Softcover reprint of the original 1st ed. 1985)
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Fourier Techniques and Applications (Paperback, Softcover reprint of the original 1st ed. 1985)
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The first systematic methods of Fourier analysis date from the
early eighteenth century with the work of Joseph Fourier on the
problem of the flow of heat. (A brief history is contained in the
first paper.) Given the initial tempera ture at all points of a
region, the problem was to determine the changes in the temperature
distribution over time. Understanding and predicting these changes
was important in such areas as the handling of metals and the
determination of geological and atmospheric temperatures. Briefly,
Fourier noticed that the solution of the heat diffusion problem was
simple if the initial temperature dis tribution was sinusoidal. He
then asserted that any distri bution can be decomposed into a sum
of sinusoids, these being the harmonics of the original function.
This meant that the general solution could now be obtained by
summing the solu tions of the component sinusoidal problems. This
remarkable ability of the series of sinusoids to describe all
"reasonable" functions, the sine qua non of Fourier analysis and
synthesis, has led to the routine use of the methods originating
with Fourier in a great diversity of areas - astrophysics,
computing, economics, electrical engineering, geophysics,
information theory, medical engineering, optics, petroleum and
mineral exploration, quan tum physics and spectroscopy, to name a
few."
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