Ramp Function

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A Ramp Function is an Unary Function defined as [math]R(x) := \max(x,0) [/math]



References

2018

  • (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Ramp_function Retrieved:2018-2-18.
    • The ramp function is a unary real function, whose graph is shaped like a ramp. It can be expressed by numerous definitions, for example "0 for negative inputs, output equals input for non-negative inputs". The term "ramp" can also be used for other functions obtained by scaling and shifting, and the function in this article is the unit ramp function (slope 1, starting at 0).

      This function has numerous applications in mathematics and engineering, and goes by various names, depending on the context.

      Definitions

      The ramp function (R(x) : ℝ → ℝ0+) may be defined analytically in several ways. Possible definitions are:

this can be derived by noting the following definition of max(a,b),
[math] \max(a,b) = \frac{a+b+|a-b|}{2} [/math]
for which a = x and b = 0
  • [math]R\left( x \right) := xH(x)[/math]
  • The convolution of the Heaviside step function with itself:
  • [math]R\left( x \right) := H(x) * H(x)[/math]
  • [math]R(x) := \int_{-\infty}^{x} H(\xi)\,d\xi[/math]
  • [math]R(x) := \langle x\rangle[/math]