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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.
You can use \ast function:
$$(f \ast g)(t):=\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$$
$$(f \ast g)(t):=\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$$
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}
$$(f \circledast g)(t):=\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$$
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:
$$
(f \ast g)[n]=\sum_{m=-\infty}^{\infty} f[m] g[n-m]
$$
$$ (f \ast g)[n]=\sum_{m=-\infty}^{\infty} f[m] g[n-m] $$