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triangularPulse

Triangular pulse function

Description

example

triangularPulse(a,b,c,x) returns the Triangular Pulse Function.

triangularPulse(a,c,x) is a shortcut for triangularPulse(a, (a + c)/2, c, x).

triangularPulse(x) is a shortcut for triangularPulse(-1, 0, 1, x).

Examples

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syms x
fplot(triangularPulse(x), [-2 2])

Figure contains an axes object. The axes object contains an object of type functionline.

Compute the triangular pulse function for these numbers. Because these numbers are not symbolic objects, you get floating-point results.

[triangularPulse(-2, 0, 2, -3)
triangularPulse(-2, 0, 2, -1/2)
triangularPulse(-2, 0, 2, 0)
triangularPulse(-2, 0, 2, 3/2)
triangularPulse(-2, 0, 2, 3)]]
ans =
         0
    0.7500
    1.0000
    0.2500
         0

Compute the same values symbolically by converting the numbers to symbolic objects.

[triangularPulse(sym(-2), 0, 2, -3)
triangularPulse(-2, 0, 2, sym(-1/2))
triangularPulse(-2, sym(0), 2, 0)
triangularPulse(-2, 0, 2, sym(3/2))
triangularPulse(-2, 0, sym(2), 3)]
ans =
   0
 3/4
   1
 1/4
   0

Use triangularPulse with one input argument as a shortcut for computing triangularPulse(-1, 0, 1, x):

syms x
triangularPulse(x)
ans =
triangularPulse(-1, 0, 1, x)

Use triangularPulse with three input arguments as a shortcut for computing triangularPulse(a, (a + c)/2, c, x):

syms a c x
triangularPulse(a, c, x)
ans =
triangularPulse(a, a/2 + c/2, c, x)

Depending on the relation between inputs, the triangularPulse has special values.

Compute the triangular pulse function for a < x < b:

syms a b c x
assume(a < x < b)
triangularPulse(a, b, c, x)
ans =
(a - x)/(a - b)

For further computations, remove the assumption by recreating the variables using syms:

syms a b x

Compute the triangular pulse function for b < x < c:

assume(b < x < c)
triangularPulse(a, b, c, x)
ans =
-(c - x)/(b - c)

For further computations, remove the assumption:

syms b c x

Compute the triangular pulse function for a = b:

syms a b c x
assume(b < c)
triangularPulse(b, b, c, x)
ans =
-((c - x)*rectangularPulse(b, c, x))/(b - c)

Compute the triangular pulse function for c = b:

assume(a < b)
triangularPulse(a, b, b, x)
ans =
((a - x)*rectangularPulse(a, b, x))/(a - b)

For further computations, remove all assumptions on a, b, and c:

syms a b c

Input Arguments

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Input, specified as a number or a symbolic scalar. This argument specifies the rising edge of the triangular pulse function.

Input, specified as a number or a symbolic scalar. This argument specifies the peak of the triangular pulse function. If you specify a and c, then (a + c)/2. Otherwise, 0.

Input, specified as a number or a symbolic scalar. This argument specifies the falling edge of the triangular pulse function.

Input, specified as a number, vector, matrix, or array, or a symbolic number, variable, array, function, or expression.

More About

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Triangular Pulse Function

If a < x < b, then the triangular pulse function equals (x - a)/(b - a).

If b < x < c, then the triangular pulse function equals (c - x)/(c - b).

If x <= a or x >= c, then the triangular pulse function equals 0.

The triangular pulse function is also called the triangle function, hat function, tent function, or sawtooth function.

Tips

  • If a, b, and c are variables or expressions with variables, triangularPulse assumes that a <= b <= c. If a, b, and c are numerical values that do not satisfy this condition, triangularPulse throws an error.

  • If a = b = c, triangularPulse returns 0.

  • If a = b or b = c, the triangular function can be expressed in terms of the rectangular function.

Introduced in R2012b