Latex convolution symbol

How to write convolution symbol using Latex ? In function analysis, the convolution of f and g f∗g is defined as the integral of the product of the two functions after one is reversed and shifted.

Write default Latex convolution symbol

You can use \ast function:

$$(f \ast g)(t):=\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$$

$$(f\ast g)(t):={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}f(\tau )g(t-\tau )d\tau$$

Latex convolution with circle using amssymb

You can use \circledast symbol from amssymb

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}

$$(f \circledast g)(t):=\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$$

\end{document}

$$(f⊛g)(t):={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}f(\tau )g(t-\tau )d\tau$$

Examples

Circular convolution:

$$\left(f \ast g_{T}\right)(t) \equiv \int_{t_{0}}^{t_{0}+T} \left[\sum_{k=-\infty}^{\infty} f(\tau+k T)\right] g_{T}(t-\tau) d\tau$$

$$(f\ast g_T)(t)\equiv {\int }_{t_0}^{t_0+T}[\sum _{k=-\mathrm{\infty }}^{\mathrm{\infty }}f(\tau +kT)]g_T(t-\tau )d\tau$$

Discrete convolution:

$$(f \ast g)[n]=\sum_{m=-\infty}^{\infty} f[m] g[n-m]$$

$$(f\ast g)[n]=\sum _{m=-\mathrm{\infty }}^{\mathrm{\infty }}f[m]g[n-m]$$