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rectangularPulse

Rectangular pulse function

Syntax

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

Description

rectangularPulse(a,b,x) returns the rectangular pulse function.

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

Input Arguments

a

Number (including infinities and symbolic numbers), symbolic variable, or symbolic expression. This argument specifies the rising edge of the rectangular pulse function.

Default: -1/2

b

Number (including infinities and symbolic numbers), symbolic variable, or symbolic expression. This argument specifies the falling edge of the rectangular pulse function.

Default: 1/2

x

Number (including infinities and symbolic numbers), symbolic variable, or symbolic expression.

Examples

Find Rectangular Pulse Function

Compute the rectangular pulse function for these numbers. Because these numbers are not symbolic objects, you get floating-point results:

[rectangularPulse(-1, 1, -2)
rectangularPulse(-1, 1, -1)
rectangularPulse(-1, 1, 0)
rectangularPulse(-1, 1, 1)
rectangularPulse(-1, 1, 2)]
ans =
         0
    0.5000
    1.0000
    0.5000
         0

Compute the rectangular pulse function for the numbers converted to symbolic objects:

[rectangularPulse(sym(-1), 1, -2)
rectangularPulse(-1, sym(1), -1)
rectangularPulse(-1, 1, sym(0))
rectangularPulse(sym(-1), 1, 1)
rectangularPulse(sym(-1), 1, 2)]
ans =
   0
 1/2
   1
 1/2
   0

Edge Values of Rectangular Pulse

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

syms a b x
assume(a < b)
rectangularPulse(a, b, a)
rectangularPulse(a, b, b)
ans =
1/2
 
ans =
1/2

For further computations, remove the assumption:

syms a b clear

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

syms a x
rectangularPulse(a, a, x)
ans =
0

Fixed Rectangular Pulse of Width 1

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

syms x
rectangularPulse(x)
ans =
rectangularPulse(-1/2, 1/2, x)
[rectangularPulse(sym(-1))
rectangularPulse(sym(-1/2))
rectangularPulse(sym(0))
rectangularPulse(sym(1/2))
rectangularPulse(sym(1))]
ans =
   0
 1/2
   1
 1/2
   0

Plot Rectangular Pulse Function

syms x
fplot(rectangularPulse(x), [-1 1])

Relation Between Heaviside and Rectangular Pulse

Call rectangularPulse with infinities as its rising and falling edges:

syms x
rectangularPulse(-inf, 0, x)
rectangularPulse(0, inf, x)
rectangularPulse(-inf, inf, x)
ans =
heaviside(-x)
 
ans =
heaviside(x)
 
ans =
1

More About

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Rectangular Pulse Function

The rectangular pulse function is defined as follows:

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

The rectangular pulse function is also called the rectangle function, box function, Π-function, or gate function.

Tips

  • 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 = b, rectangularPulse returns 0.

Introduced in R2012b

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