Triangle Function
TriangleFunction
The triangle function is the function
where Pi(x) is the rectangle function, H(x) 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].
TriangleFunction3D
There is also a three-argument function known as the triangle function,
| lambda(x,y,z)=x^2+y^2+z^2-2xy-2xz-2yz. |
(4)
|
It follows that
| lambda(a^2,b^2,c^2)=(a+b+c)(a+b-c)(a-b+c)(a-b-c). |
(5)
|
See also
Absolute Value, Bartlett Function, Heaviside Step Function, Ramp Function, Rectangle Function, Sign, Triangle Coefficient, Triangle Wave, Triangular DistributionExplore with Wolfram|Alpha
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References
Bracewell, R. "The Triangle Function of Unit Height and Area, Lambda(x)." In The Fourier Transform and Its Applications, 3rd ed. New York: McGraw-Hill, p. 53, 1999.Referenced on Wolfram|Alpha
Triangle FunctionCite this as:
Weisstein, Eric W. "Triangle Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TriangleFunction.html