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,

Missing Image:img src="SP7-f_files/113Ftran1.html"where u is the new

variable of the transform F(u) and i² = -1. If the Fourier transform of a function is known, the function itself may be recovered by use of the inversion formula:

Missing Image:img src="SP7-f_files/113Ftran2.html"

</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