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Fourier Transform--Ramp Function

Let $R(x)$ be the Ramp Function, then the Fourier Transform of $R(x)$ is given by

\begin{displaymath}
{\mathcal F}[R(x)]=\int_{-\infty}^\infty e^{-2\pi ikx}R(x)\,dx = \pi i\delta'(2\pi k)-{1\over 4\pi^2 k^2},
\end{displaymath}

where $\delta'(x)$ is the Derivative of the Delta Function.

See also Ramp Function




© 1996-9 Eric W. Weisstein
1999-05-26