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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])

Figure contains an axes object. The axes object contains an object of type functionline.

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