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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

F_x[R(x)](k)=int_(-infty)^inftye^(-2piikx)R(x)dx
(1)
=i/(4pi)delta^'(k)-1/(4pi^2k^2),
(2)

where delta^'(x) is the derivative of the delta function.

See also

Ramp Function

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Cite this as:

Weisstein, Eric W. "Fourier Transform--Ramp Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FourierTransformRampFunction.html

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