Convolution Calculator

Enter continuous-time signals \(x(t)\) and \(h(t)\) using the notation below.

$$ y(t)=\int_{-\infty}^{\infty}x(\tau)h(t-\tau)\,\mathrm d\tau $$

You get plots of \(x(t)\), \(h(t)\), and their output \(y(t)=x(t)*h(t)\) instantly. Example: \(\mathrm{rect}(t) * \mathrm{tri}(t)\). See step-by-step overlap (Dynamic Explorer). Use the Dynamic Explorer to slide \(t\) and visualize the overlap \(x(\tau)\cdot h(t-\tau)\).

*
Supported notation & limits
Primitives/synonyms: \(\mathrm{rect}\), \(\mathrm{tri}\), \(\sin\), \(\cos\), \(\exp\), \(\mathrm{step}\) / \(u(t)\) / \(\mathrm{heaviside}\), \(\delta\) / \(\delta\), \(\mathrm{sign}\), \(\mathrm{si}\).
Syntax: use \( * \) for multiplication and parentheses, e.g. \(\sin(\pi t) * u(t)\).
Limits: complex piecewise expressions may fail, finite plotting range is used, and numeric resolution affects sharp transitions in \(y(t)\).