15.2.2 Rectangle function: rect

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 ‍15.2.1) for a=−1/2 and b=1/2.

• rect takes one argument:
  x, an identifier or an expression.
• rect(x) returns the value of the rectangle function at x.

Example.
Input:

Output:

To compute the convolution of the rectangle function with itself, you can use the convolution theorem.
Input:

Output:

This result is the triangle function tri(x) (see section ‍15.2.3).