I finally got around to registering a domain name in the middle of 2006, so by then, most of the “cool” names were gone. In fact, almost any common term in the .com, .net or .org namespace was gone. So, when I learned that unitstep.net was still available, I jumped on it, since after all, I am in Electrical Engineering.
The unit step
But just what is the unit step? (Or just “unitstep”, as I’ve now taken to calling it.) Well, if you read the Wikipedia article, you’ll get a very technical and mathematical definition. Basically, a unit step is a function that “turns on” at x = 0; thus for x < 0, the function has a value of 0, and for x > 0, the function’s value is 1. Precisely at x = 0, the function is usually defined to have a value of 1/2. Sometimes, however, the value right at 0 is not defined or otherwise ignored, however in some cases (i.e. for symmetry reasons), the value of 1/2 at x = 0 is applied. The general shape of the unit step function is enshrined in the header graphic of my site.
The unit step is also known as the Heaviside function. But heaviside.net doesn’t have the same ring to it – and it’s probably already taken, but I didn’t check. The unit step also seems like a pretty plain function, since it doesn’t have any curves or a weird shape. But, it’s actually pretty useful in the field of signal processing, for testing the response of a system. For example, when testing how long it takes for a capacitor to build up its voltage from 0 V to the applied level, one is really applying a sort of “unit step” to it. You can imagine flipping the switch on the voltage source as being a unit step function on the voltage level; right before it’s switched on, the voltage is zero, and right after, it’s whatever the voltage source level is.
A useful step
The unit step is probably only second to the unit impulse (or delta dirac function) in terms of basic signals in electrical engineering. (The unit impulse is the derivative of the unit step function.) But again, unitimpulse.net or delta-dirac-function.net just doesn’t have the same ring.
