Making explicit something implicit in steven0461′s comment: the term “delta function” has a technical meaning, and it doesn’t have anything to do with what you’re describing. You might therefore prefer to avoid using that term in this context.
(The “delta function” is a mathematical object that isn’t really even a function; handwavily it has f(x)=0 when x isn’t 0, f(x) is infinite when x is 0, and the total area under the graph of f is 1. This turns out to be a very useful gadget in some areas of mathematics, and one can turn the handwaving into actual mathematics at some cost in complexity. When handwaving rather than mathematics is the point, one sometimes hears “delta function” used informally to denote anything that starts very small, rapidly becomes very large, and then rapidly becomes very small again. Traffic at a web site when it gets a mention in some major media outlet, say. That’s the “Dirac delta” Steven mentioned; the “Kronecker delta” is a function of two variables that’s 1 when they’re equal and 0 when they aren’t, although most of the time when it’s used it’s actually denoting something hairier than that. This isn’t the place for more details.)
Making explicit something implicit in steven0461′s comment: the term “delta function” has a technical meaning, and it doesn’t have anything to do with what you’re describing. You might therefore prefer to avoid using that term in this context.
(The “delta function” is a mathematical object that isn’t really even a function; handwavily it has f(x)=0 when x isn’t 0, f(x) is infinite when x is 0, and the total area under the graph of f is 1. This turns out to be a very useful gadget in some areas of mathematics, and one can turn the handwaving into actual mathematics at some cost in complexity. When handwaving rather than mathematics is the point, one sometimes hears “delta function” used informally to denote anything that starts very small, rapidly becomes very large, and then rapidly becomes very small again. Traffic at a web site when it gets a mention in some major media outlet, say. That’s the “Dirac delta” Steven mentioned; the “Kronecker delta” is a function of two variables that’s 1 when they’re equal and 0 when they aren’t, although most of the time when it’s used it’s actually denoting something hairier than that. This isn’t the place for more details.)