# Fourier transform

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Fourier transform
a mapping of a function, as a signal, that is defined in one domain, as space or time, into another domain, as wavelength or frequency, where the function is represented in terms of sines and cosines.
[1920-25; see FOURIER ANALYSIS]

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In mathematical analysis, an integral transform useful in solving certain types of partial differential equations.

A function's Fourier transform is derived by integrating the product of the function and a kernel function (an exponential function raised to a negative complex power) over the interval from -∞ to +∞. The Fourier transform of a function g is given by
. Such transforms, discovered by Joseph Fourier, are particularly useful in studying problems concerning electrical potential.

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in mathematics, a particular integral transform. As a transform of an integrable complex-valued function f of one real variable, it is the complex-valued function f ˆ of a real variable defined by the following equation

In the integral equation

the function f (y) is an integral transform of F(x), and K(x,y) is the kernel. Often the reciprocal relationship is valid:

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Universalium. 2010.

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