\circledast - LaTeX Symbol

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⊛

\circledast

The \circledast symbol is used to denote a convolution operation in mathematics, particularly in the context of functions and signals. It represents the integral of the product of two functions after one is reversed and shifted, commonly used in signal processing and analysis.

Examples

(f ⊛ g) (t) = \int_{- \infty}^{\infty} f (τ) g (t - τ) d τ

Convolution of two functions f and g over time t.

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

h (t) = (x ⊛ y) (t)

Convolution of signals x and y resulting in signal h.

h(t) = (x \circledast y)(t)

(f ⊛ g) (x) = n = - \infty \sum \infty f (n) g (x - n)

Discrete convolution of sequences f and g.

(f \circledast g)(x) = \sum_{n=-\infty}^{\infty} f(n) g(x-n)