**Convolution**

The convolution $h$ of two
functions $f$ and $g$ is defined by

$$h(x) \equiv \int_{-\infty}^\infty
f(u) g(x - u) du$$

and the convolution operator is often indicated by
the symbol $\otimes$, so the above equation can be written

$$h = f \otimes g$$

This figure indicates that convolution involves taking the mirror image of $g$, overlaying it on $f$, sliding $g$ from left to right, and measuring the overlap of $f$ and $g$. Convolution is a smoothing operation that smears one function with another. It is often used in conjunction with Fourier transforms because the convolution theorem can simplify the calculation of Fourier transforms.