Why is 0 and 30 1/2?

Trying to plot the function x[n] = u[n] - u[n-30]. I'm getting 1/2 for n=0 and n=30. The correct answer is 1 from 0-29 and 0>=30, right? Below is my code and the result. I've tried heaviside(sym(n)) - heaviside(sym(n-30)) and I get the same result (I don't really know the differnce between using sym and not).

Answer 1

[Walter Roberson]

heaviside(X) by default has a value of 1/2 when X has a value of 0

The Heaviside function does not have a well-defined value at 0 exactly. There are at least three different values for Heaviside(0) that are useful in practice: 0, 1, and 1/2 . When you reach 30, then has the value "not yet jumped", or has it "already jumped", or is in "in the process of jumping" ? Is the glass half-full or is it half-empty ?

You can use sympref('HeavisideAtOrigin') to change the value that heaviside(0) will return.

[Alexander Bearon]

Do you mind showing me how to implement this? I keep getting the error Index in position 1 exceeds array bounds (must not exceed 1)

[Steven Lord]

See the second example on the sympref documentation page.

[Walter Roberson]

sympref("HeavisideAtOrigin", 1)

ans = 

n = 0:30;
xn = heaviside(n) - heaviside(n-30);
stem(n, xn)

[Walter Roberson]

If you get an error with

sympref('HeavisideAtOrigin', 1)

then you might possibly be using a version of MATLAB before R2015a.

Answer 2

[David Goodmanson]

Hi Alexander;

This occurs because

heaviside(-.3:.1:.3)
ans =   0         0         0    0.5000    1.0000    1.0000    1.0000

The value of this function at 0 equals 1/2, not 0 or 1.