Candid Tools

Laplace Weighting Lens

Laplace Weighting Lens visualizes exponential weighting, rotation and transform convergence with linked graphs, entirely in your browser.

Shape the lens

f(t) = exp(−t)
0.6
1
10

Your sample s

0.6 + 1i

Finite estimate · 0 to 10

0.4494 − 0.2809i

Infinite-time transform

0.4494 − 0.2809i
The signal through your lensf(t)Real contributionImaginary contribution
0-0.36282.50.0143950.39167.50.7688101.146TimeAmplitude

Grey is the original signal. Weighting changes its envelope; rotation splits it into real and imaginary contributions.

Accumulated integralReal sumImaginary sum
0-0.40272.5-0.15450.094727.50.3435100.5922TimeAmplitude

Distance from the exact transform: 3.08e-6. Includes window truncation and quadrature error.

0
Choose s · shaded region converges
-3-3-2-2-1-1112233ReIm

Drag the gold point, or use the σ and ω sliders.

The sum draws a path in the complex planeWhole windowAnimated accumulation
0-0.40270.25-0.27210.5-0.14140.75-0.0106910.12Real accumulated valueImaginary accumulated value

At t = 0, the rotating contribution is 1 + 0i.

F(s) = ∫₀∞ f(t) exp(−st) dt
For this signal: F(s) = 1 / (s + 1)

At a glance

Accepts
Six causal signal presets, real and imaginary parts of s, a 2–16 time-unit window
Outputs
Weighted signals, a complex accumulation path, finite-window estimates and exact preset transforms
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 functions only; midpoint quadrature with 1,600 intervals; a finite window is not an infinite-time transform
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

The unilateral Laplace transform adds f(t) × exp(−σt) × exp(−iωt) from zero to infinity. σ changes the exponential weighting; ω rotates each contribution clockwise in the complex plane.

The shaded region is the region of convergence for the chosen causal signal. A finite-window integral always gives a finite number here, even outside that region; that number is not an infinite-time transform. Increase the window to see the difference.

Try exponential growth with σ = 0.6, then raise σ above 1. For a pulse, the integration interval is finite, so every finite s is allowed.

Reference: University of Utah Laplace transform notes

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.