The *Fourier transform* of a real- or complex-valued function f(t) is defined by

Latex |
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```
\[\mathscr{F}\left(f\right)\left(x\right)=\mathscr{F}\mskip-3.0mu f\mskip 3.0mu %
\left(x\right)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}f(t)e^{ixt}\mathrm{%
d}t.\]
``` |