Fourier Transform--Ramp Function

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

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

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

See also Ramp Function