Convolution Machine

Convolution Machine animates the signed overlap of two causal signals and shows their Laplace transform product, entirely in your browser.

Two signals, one output

First signal f(t)Second signal g(t)

f(t) = 1 for 0 ≤ t < 2; otherwise 0
f(t) = exp(−t)

1 · Flip and slidef(τ)g(t − τ)

The purple curve is reversed and shifted. Its causal support ends at τ = t.

2 · Multiply the overlapf(τ) × g(t − τ)

Signed overlap area

y(0) ≈ 0

3 · Accumulate the outputy(t) = f ∗ gRecorded so far

Slide time t0

At a glance

Accepts: Two signals chosen from pulse, exponential decay, unit step and sine presets
Outputs: Flipped and shifted signal, overlap product, output curve and exact transform product
Where it runs: Entirely in your browser, on your device
What leaves your device: No calculation inputs are uploaded; standard site usage analytics still apply
Limits: Preset signals; a 10 time-unit view; time-domain output is numerical; Laplace samples use positive real parts
Account: Not required - there is no sign-up
Price: Free, with no watermark and no usage cap
Made by: Visrut
Last updated: 14 October 2026

What to notice

For causal signals, convolution is y(t) = ∫₀ᵗ f(τ)g(t − τ)dτ. First flip g, then shift it by t, multiply where the signals overlap, and add the signed area.

The output graph records that area for each t. A pulse through an exponential decay rises while the pulse is active, then decays after it ends. Negative overlap subtracts from the output.

In the Laplace domain, Y(s) = F(s)G(s), wherever both transforms converge. The product here is evaluated from exact preset transforms; the time-domain curve uses numerical quadrature.

Reference: Laplace transform properties and convolution

Frequently asked questions

Does this upload my inputs?

The graphs and calculations run locally in your browser. There is no account or external calculation service.

Is this a symbolic Laplace calculator?

These are visual learning tools with causal presets, zero initial conditions and numerical simulations. They do not solve arbitrary symbolic expressions. Finite-window estimates are labelled separately from infinite-time transforms.