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# triangularPulse

Triangular pulse function

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```triangularPulse(a, b, c, x)
triangularPulse(a, c, x)
```

## Description

triangularPulse(a, b, c, x) represents the triangular 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).

triangularPulse represents the triangular pulse function. This function is also called the triangle function, hat function, tent function, or sawtooth function.

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 < x < b, the triangular function equals (x - a)/(b - a). If b < x < c, the triangular function equals (c - x)/(c - b). Otherwise, it equals 0. See Example 1 and Example 2.

If a = b or b = c, the triangular function can be expressed in terms of the rectangular function. See Example 3.

If a = b = c, triangularPulse returns 0. See Example 4.

triangularPulse(x) is equivalent to triangularPulse(-1, 0, 1, x). See Example 5.

triangularPulse(a, c, x) is equivalent to triangularPulse(a, (a + c)/2, c, x). See Example 6.

triangularPulse also accepts infinities as its arguments. See Example 9.

triangularPulse and tripulse are equivalent.

## Examples

### Example 1

Compute the triangular pulse function for these input arguments:

```[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)]```

### Example 2

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

`triangularPulse(a, b, c, x) assuming a < x < b`

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

`triangularPulse(a, b, c, x) assuming b < x < c`

### Example 3

Compute the triangular pulse function for a = b and c = b:

`triangularPulse(b, b, c, x) assuming b < c`

`triangularPulse(a, b, b, x) assuming a < b`

### Example 4

For a = b = c, the triangular pulse function returns 0:

`triangularPulse(a, a, a, x)`

### Example 5

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

`triangularPulse(x)`

```[triangularPulse(-10), triangularPulse(-3/4), triangularPulse(0),
triangularPulse(2/3), triangularPulse(1)]```

### Example 6

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

`triangularPulse(a, c, x)`

```[triangularPulse(-10, 10, 3), triangularPulse(-1/2, -1/4, -2/3), triangularPulse(2, 4, 3),
triangularPulse(2, 4, 6), triangularPulse(-1, 4, 0)]```

### Example 7

Rewrite the triangular pulse function in terms of the Heaviside step function:

`rewrite(triangularPulse(a, b, c, x), heaviside)`

### Example 8

Plot the triangular pulse function:

`plot(triangularPulse(x), x = -2..2)`

### Example 9

Plot the triangular pulse function for which the argument c is a positive infinity:

`plot(triangularPulse(-1, 1, infinity, x))`

## Parameters

 a, b, c, x

## Return Values

Arithmetical expression.