Convolution visualizer

See convolution as it actually works. Pick two signals f and g, then slide g across f and watch the overlap build up the convolution y(t) = ∫ f(τ)·g(t−τ) dτ.

Flip, slide, multiply, integrate

Convolution flips one signal, slides it by t, multiplies the overlap point by point, and integrates. The shaded area in the top plot is that product; its total area is the value of the convolution at the current shift, traced out in the bottom plot.

Frequently asked questions

What is convolution?
Convolution combines two signals into a third: y(t) = ∫ f(τ)·g(t−τ) dτ. Convolving an input with a system's impulse response gives the system's output, which is why it is central to signals and linear time-invariant systems.
How does the flip-and-slide method work?
One signal is flipped in time and slid across the other. At each shift you multiply the overlapping parts and integrate the product; that area is the value of the convolution at that shift. This tool animates the flip, slide, multiply, and integrate steps.
What is convolution used for?
It models filtering, echo and reverb, image blurring, moving averages, and the response of any linear time-invariant system to an arbitrary input signal.
Is this convolution visualizer free?
Yes, it is free and runs in your browser.

See also: Fourier transform · Step/impulse response · Bode plot