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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.

Overloaded By

x

See Also

MuPAD Functions

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