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

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

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

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 the rectangular pulse function:

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

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

expand all

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.

Was this topic helpful?