Triangle Function

The triangle function is the function

			(1)
			(2)
			(3)

where  is the rectangle function,  is the Heaviside step function, and  denotes convolution. An obvious generalization used as an apodization function goes by the name of the Bartlett function.

The piecewise version of the triangle function is implemented in the Wolfram Language as UnitTriangle[x], while the generalized function version is implemented as HeavisideLambda[x].

There is also a three-argument function known as the triangle function,

(4)

It follows that

(5)

REFERENCES:

Bracewell, R. "The Triangle Function of Unit Height and Area, ." In The Fourier Transform and Its Applications, 3rd ed. New York: McGraw-Hill, p. 53, 1999.