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# 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:

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


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

## 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}


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

## Examples

Circular convolution:

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


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

Discrete convolution:

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


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