Convolution: A mathematical operation that combines features of two functions to produce a new one.
The convolution of two functions f(x) and g(x) is a mathematical operation that combines the features of both functions to produce a new function h(x). It is denoted by the symbol ∗ and defined as:
h(x) = (f ∗ g)(x) = ∫ f(t)g(x - t) dt
where the integral is taken over the entire range of both functions. In simpler terms, convolution can be thought of as flipping one function (g) and sliding it over the other function (f), multiplying the overlapping parts at each position, and adding the products together.
Convolution has wide-ranging applications in various fields, including signal processing, image processing, and scientific computing. It is particularly useful for filtering signals, extracting features, and identifying patterns in data.