Convolution Explorer

Interactive visualization of convolution — flip, shift, multiply, and integrate two signals to trace the output.

This interactive convolution visualization makes the operation at the heart of signals, systems, and neural networks concrete. Convolution combines two signals into a third, defined by $y(t) = \int f(\tau),g(t-\tau),d\tau$, and the animation breaks it into four moves you can watch: flip one signal, shift it by $t$, multiply it against the other, and integrate the overlapping area to get a single output value.

As you sweep the shift $t$, the flipped-and-shifted kernel slides across the stationary signal, the overlapping product is shaded in, and its area is traced out point by point to build the output curve below. The result panel shares the same horizontal axis as the process panel, so you see cause and effect at once — where the signals overlap most, the output peaks.

Try the trapezoid, triangle, and RC-smoothing presets to see how the shapes of the inputs determine the shape of the output, and how convolution with a smoothing kernel blurs sharp features. A metric tile verifies the theoretical property that the area under the output equals the product of the areas of the two inputs. Play the animation continuously, step through it at your own pace, or drag directly on either plot to scrub the shift and feel how convolution works.