B.12 TRIANGLE AND RAMP FUNCTIONS

Definition: Triangle Function The triangle function is

(B.60) Numbered Display Equation

The symbol inline is sometimes used.

The rectangle function is used above to specify the support of tri(x), by appropriately truncating 1−|x|. The triangle function can be derived by convolving two rectangle functions:

(B.61) Numbered Display Equation

Definition: Ramp Function The ramp function is

(B.62) Numbered Display Equation

The unit-step function in the second expression defines the support of R(x) by truncating the linear function g(x) = x. The ramp function is obtained by integrating the unit-step function:

(B.63) Numbered Display Equation

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