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



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

https://dlmf.nist.gov/1.14