About: Convolution slides one function over another, multiplying pointwise and integrating — a weighted running average. The Dirac delta δ(t) is the identity element: (f★δ)(t) = f(t). It has unit area but zero width — formally a distribution, not a function. Convolution is the mathematical foundation of linear filtering, LTI system responses, probability (sum of independent RVs), and the central limit theorem (repeated convolution → Gaussian). In frequency space, convolution becomes multiplication: F{f★g} = F̂·Ĝ.