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)
|
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.
Weisstein, Eric W. "Triangle Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/TriangleFunction.html
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