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Rectangular pulse function

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.


rectangularPulse(a, b, x)


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.


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(-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))


a, b, x

Arithmetical expressions.

Return Values

Arithmetical expression.

Overloaded By


See Also

MuPAD Functions

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