Fourier Transform
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Fourier Transform
</dt>
An analytical transformation of a function f(x) obtained (if it
exists) by multiplying the function by e^{-iux} and integrating
over all x,
variable of the transform F(u) and i^{2} = -1. If the Fourier transform of a function is known, the function itself may be recovered by use of the inversion formula:
</dd>
'The Fourier transform has the same uses as the Fourier
series: for example, the integrand F(u) exp (iux) is a solution of
a given linear differential equation, so that the integral sum of these
solutions is the most general solution of the equation.
'</dd>
'When the variable u is complex, the Fourier transform is equivalent to the
Laplace
transform.
'</dd>
'See Fourier
integral, spectral
function.
</dd>
References
This article is based on NASA's Dictionary of Technical Terms for Aerospace Use