# 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])

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.

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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.