When your phone removes background noise from a call, it is blending two signals together with an operation called convolution. Convolution combines two functions into a third that measures how much one overlaps the other as it slides past: (f ∗ g)(t) = ∫ f(τ)g(t−τ) dτ. In plain words, flip one signal backwards, slide it across the other, and at each position multiply-and-add — the result is a smoothed blend.

The discrete version is what every audio equalizer, camera blur filter, and noise-cancelling headphone computes thousands of times per second: each output sample is a weighted average of neighboring input samples. Convolution also has a famous shortcut, the convolution theorem: convolution in the time domain equals plain multiplication in the frequency domain, which is why fast Fourier transforms make real-time audio processing possible. Enter the two sequences or function samples and the calculator performs the flip-slide-multiply-add to return the convolved output.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Convolution Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.