DefinitionDelta functions are defined as δ(x) and are zero everywhere but x = 0, and infinite across all values of x except for x = 0 where their integral across the entire real line is 1. Delta functions or impulse functions are useful in many physics and engineering settings including representation in signal processing, it’s often called an impulse or unit impulse in the engineering. And it’s commonly useful as a distribution, which is a concept from the theory of distributions used to generalise functions and solve differential equations as an example. The delta function δ(x) satisfies the following properties where the integral of δ(x) across the real line is equal to 1, and the integral of a constant multiplied by the delta function is equal to the constant evaluated at zero, respectively.
