 
 
 
21.1.2  Rectangle function
The rectangle function Π is 0 everywhere except on [−1/2,1/2],
where it is 1; namely,
Π(x)=θ(x+1/2)−θ(x−1/2)
where θ is the 
Heaviside function. The rectangle function is a special case of boxcar function
(see Section 21.1.1) for a=−1/2 and b=1/2.
The rect
command computes the rectangle function.
- 
rect takes
x, an identifier or an expression.
- rect(x) returns the value of the rectangle function
at x.
Example
|  | | | θ | ⎛ ⎜
 ⎜
 ⎝
 |  | + |  | ⎞ ⎟
 ⎟
 ⎠
 | −θ | ⎛ ⎜
 ⎜
 ⎝
 |  | − |  | ⎞ ⎟
 ⎟
 ⎠
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
To compute the convolution of the rectangle function with itself, you
can use the Convolution Theorem (see Section 21.4.2).
| R:=fourier(rect(x),x,s):; ifourier(R^2,s,x) | 
|  | | | −2 x θ | ⎛ ⎝
 | x | ⎞ ⎠
 | +x θ | ⎛ ⎝
 | x+1 | ⎞ ⎠
 | +x θ | ⎛ ⎝
 | x−1 | ⎞ ⎠
 | +θ | ⎛ ⎝
 | x+1 | ⎞ ⎠
 | −θ | ⎛ ⎝
 | x−1 | ⎞ ⎠
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
This result is the triangle function  tri(x)  (see section 21.1.3).
 
 
