What does "H" mean?!

jaja1990

I have this question in my assignment paper:-

8. Sketch the graph of:
(a)
y = |2x − 2|;
(b)
y = 2H(x − 4)

(a) is obvious, but how do I sketch (b)? Does "H" stand for some specific constant?

JJacquelin

Possibly, the Heaviside step function H(x)
http://mathworld.wolfram.com/HeavisideStepFunction.html

jaja1990

The webpage in the link you've given says:-
The function is:-
0 when x < 0,
1/2 when x = 0,
1 when x > 0.
But here: http://simple.wikipedia.org/wiki/Heaviside_Function, defines the function as:-
1 when x => 0,
0 when x < 0.

To begin with, which should I follow?

JJacquelin

I think that H(0)=0 correponds to an old definition remaining from history and that the standard definition is with H(0)=1/2.
Generally this is of no consequence in partical applications.

chiro

If one wanted to use an approximation like a fourier series version, then it makes sense to define H(0) as 1/2 based on properties of fourier series when you have this kind of 'Gibbs' phenomenon.