What’s the name of the mathematical function whose value is zero almost everywhere but 1 or some constant value in a finite region, maybe:
y = 1 if -1 < x < +1, else y = 0
or at least anything that is a single rectangular pulse?
We were thinking “Heaviside”, but that’s a step that is 1 for all x>0, it never goes back down.
The function you describe is the indicator function of the interval (-1,1). Indicator functions are special cases of step functions.
They’re also commonly known as characteristic functions. Given a subset E of some given domain, the characteristic function of E is defined to be 1 at points in E, and 0 elsewhere.
Characteristic! That’s the word I meant. Indicator is for random variables, sorry.
Well, you can get that function by multiplying Heaviside functions. Consider f(x) = H(x - 1)H(1 - x). It’s equal to one for -1 < x < 1 and 0 elsewhere.
It’s also sometimes called a top-hat function, or a square pulse.
In signal analysis, I’ve heard it called a Boxcar function, or Rectangular window.
Or f(x) = H(x + 1) - H(x - 1).
I don’t think there’s anything wrong with the term “rectangular pulse function”.
Or even “inverse sinc function”.
H(x + 1) - H(x - 1) = L[sup]-1[/sup]{sin(ω/2)/(ω/2)}
Or even “inverse sinc function”.
H(x + 1) - H(x - 1) = L[sup]-1[/sup]{sin(ω/2)/(ω/2)}
On second thought, “inverse sinc function” is too ambiguous to be very useful.
On second thought, “inverse sinc function” is too ambiguous to be very useful.