The ramp function is defined by
(1)
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(2)
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(3)
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(4)
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where is the Heaviside step function and denotes convolution.
It is implemented in the Wolfram Language as Ramp[x].
The derivative is
(5)
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The Fourier transform of the ramp function is given by
(6)
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(7)
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where is the delta function and its derivative.