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rectangularPulse

Rectangular pulse function

Description

example

rectangularPulse(a,b,x) returns the Rectangular Pulse Function.

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

Examples

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Plot the rectangular pulse function using fplot.

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

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 same numbers in symbolic form.

[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

Show that 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 assumptions on the variables by recreating them using syms:

syms a b

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

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

Compute a rectangular pulse of width by using rectangularPulse(x). This call is equal to 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

When the rising or falling edge of rectangularPulse is Inf, then the result is in terms of heaviside.

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

Input Arguments

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Input, specified as a number or a symbolic scalar. This argument specifies the rising edge of the rectangular pulse function.

Input, specified as a number or a symbolic scalar. This argument specifies the falling edge of the rectangular pulse function.

Input, specified as a number, vector, matrix, or array, or a symbolic number, variable, array, function, or expression.

More About

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Rectangular Pulse Function

  • 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, boxcar function, Pi 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