rectangularPulse

Rectangular pulse function

Syntax

r = rectangularPulse(a,b,x)

r = rectangularPulse(x)

Description

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

r = rectangularPulse(x) is the same as rectangularPulse(-1/2,1/2,x).

Examples

Compute Rectangular Pulse Function

Compute the rectangular pulse function at coordinates –2, –1, 0, 1, and 2 with specified rising and falling edge at –1 and 1. Because these inputs are not symbolic objects, you get floating-point results.

r = rectangularPulse(-1,1,-2:2)

r = 1×5

         0    0.5000    1.0000    0.5000         0

Compute the rectangular pulse function for the same inputs in symbolic form.

r = rectangularPulse(sym(-1),1,-2:2)

r = 
$$\left(\begin{array}{ccccc}0& \frac{1}{2}& 1& \frac{1}{2}& 0\end{array}\right)$$

Plot Rectangular Pulse Function

Plot the rectangular pulse function using fplot.

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

Edge Values of Rectangular Pulse

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)
r = rectangularPulse(a,b,a)

r = 
$$\frac{1}{2}$$

r = rectangularPulse(a,b,b)

r = 
$$\frac{1}{2}$$

For further computations, remove the assumptions on the variables a and b by recreating them using syms.

syms a b

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

r = rectangularPulse(a,a,x)

r = $$0$$

Change Values of Rectangular Pulse at Rising and Falling Edges

The default value of the rectangularPulse function at the rising and falling edges is 1/2.

syms a b
assume(a < b)
r = rectangularPulse(a,b,a)

r = 
$$\frac{1}{2}$$

r = rectangularPulse(a,b,b)

r = 
$$\frac{1}{2}$$

Another common value at these edges is 1. To change the value of rectangularPulse at the edges, use sympref to set the value of the 'HeavisideAtOrigin' preference. Store the previous parameter value returned by sympref, so that you can restore it later.

oldparam = sympref('HeavisideAtOrigin',1);

Check the new value of rectangularPulse at the rising and falling edges.

r = rectangularPulse(a,b,a)

r = $$1$$

r = rectangularPulse(a,b,b)

r = $$1$$

The preferences set by sympref persist throughout your current and future MATLAB® sessions. To restore the previous value of rectangularPulse at the edges, use the value stored in oldparam.

sympref('HeavisideAtOrigin',oldparam);

Alternatively, you can restore the default value of 'HeavisideAtOrigin' by using the 'default' setting.

sympref('HeavisideAtOrigin','default');

Relation Between Rectangular Pulse and Heaviside Function

When the rising or falling edge of rectangularPulse is at the infinity, then this function is the same as the Heaviside step function (the unit step function).

syms x
r = rectangularPulse(-Inf,0,x)

r = $$\mathrm{heaviside}\left(-x\right)$$

r = rectangularPulse(0,Inf,x)

r = $$\mathrm{heaviside}\left(x\right)$$

Input Arguments

a — Starting position of rectangular pulse

-1/2 (default) | number | symbolic scalar variable

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

b — Ending position of rectangular pulse

1/2 (default) | number | symbolic scalar variable

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

x — Input coordinates

number | vector | matrix | array | symbolic number | symbolic variable | symbolic array | symbolic function | symbolic expression

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

More About

Rectangular Pulse Function

• The rectangular pulse function returns 1 if the input coordinates x are within the specified interval range a < x < b.

• The rectangular pulse function, by default, returns ½ at the edges of the specified interval where x = a or x = b (a must not equal to b). To change the default value of the rectangular pulse at the edges, you can use sympref. For more details, see Change Values of Rectangular Pulse at Rising and Falling Edges.

• Otherwise, the rectangular pulse function returns 0.

The rectangular pulse function is also known as the rectangular function, normalized boxcar function, Heaviside 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.

Version History

Introduced in R2012b