# rectangularPulse

Rectangular pulse function

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```rectangularPulse(`a`, `b`, `x`)
rectangularPulse(`x`)
```

## Description

`rectangularPulse(a, b, x)` represents the rectangular function.

`rectangularPulse(x)` is a shortcut for ```rectangularPulse(-1/2, 1/2, x)```.

The rectangular function is also called the rectangle function, box function, Pi function, or gate function.

If `a` and `b` are variables or expressions with variables, `rectangularPulse` assumes that `a < b`. If `a` and `b` are numerical values, such that `a > b`, `rectangularPulse` throws an error.

If `a < x < b`, the rectangular pulse function equals 1. If `x = a` or `x = b`, the rectangular pulse function equals 1/2. Otherwise, it equals 0. See Example 1 and Example 2.

If `a = b`, `rectangularPulse` returns 0. See Example 3.

`rectangularPulse(x)` is equivalent to ```rectangularPulse(-1/2, 1/2, x)```. See Example 4.

`rectangularPulse` also accepts infinities as its arguments. See Example 7.

`rectangularPulse` and `rectpulse` are equivalent.

## Examples

### Example 1

Compute the rectangular pulse function for these input arguments:

```[rectangularPulse(-1, 1, -2), rectangularPulse(-1, 1, -1), rectangularPulse(-1, 1, 0), rectangularPulse(-1, 1, 1), rectangularPulse(-1, 1, 2)]```

### Example 2

If `a < b`, the rectangular pulse function for `x = a` and `x = b` equals 1/2:

```assume(a < b); [rectangularPulse(a, b, a), rectangularPulse(a, b, b)]```

### Example 3

For `a = b`, the rectangular pulse function returns 0:

`rectangularPulse(a, a, x)`

### Example 4

Use `rectangularPulse` with one input argument as a shortcut for computing `rectangularPulse(-1/2, 1/2, x)`:

`rectangularPulse(x)`

```[rectangularPulse(-1), rectangularPulse(-1/2), rectangularPulse(0), rectangularPulse(1/2), rectangularPulse(1)]```

### Example 5

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

`rewrite(rectangularPulse(a, b, x), heaviside)`

### Example 6

Plot the rectangular pulse function:

`plot(rectangularPulse(x), x = -1..1)`

### Example 7

Plot the rectangular pulse function for which the argument `b` is a positive infinity:

`plot(rectangularPulse(0, infinity, x))`

## Parameters

 `a`, `b`, `x` Arithmetical expressions.

## Return Values

Arithmetical expression.

`x`

## See Also

### MuPAD Functions

Was this topic helpful?

Get trial now