PPolySim OS

Wavelet Transform

See a signal split into scales. A real discrete wavelet transform decomposes, denoises by thresholding detail coefficients, and reconstructs — all live in your browser.

Wavelet Transform StudioLive

Controls

Signal

Wavelet

Decompose a signal into scales with a real DWT, then threshold the detail coefficients to denoise it. Watch the scalogram lose its faint noise while the strong edges survive.

Presets

▶ Run in Python

Data Inspector

Waveletdb4
Levels4
Coeffs kept48%
Recon error31.4%
Roundtrip1.4e-12

Governing equation

Reading this result: Thresholding zeroed the small detail coefficients — these mostly encode noise, which spreads thinly across all coefficients, while genuine edges and features concentrate into a few large ones. Keeping just 48% of the detail coefficients reconstructs the underlying signal with 31.4% relative error. Push the threshold too high and you start erasing real structure, not just noise.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →
★ Sign in to save this setup
Save your tuned setup, or drop this simulation into your own site, docs, or course page.

How it works

The discrete wavelet transform (DWT) runs a signal through a filter bank: a low-pass and high-pass filter followed by downsampling, repeated on the approximation to build the Mallat pyramid. Unlike the Fourier transform, wavelets localize in BOTH time and frequency, so a sharp edge shows up as a few large coefficients at a specific place and scale rather than being smeared across every frequency. This studio implements Haar and Daubechies-4 with periodic boundaries (the transform roundtrips to machine precision). Thresholding the detail coefficients — soft or hard — zeroes the many small coefficients that noise produces while keeping the few large ones that encode real edges, then the inverse DWT reconstructs a denoised signal. The scalogram shows coefficient magnitude across scale and position, so you can watch the multiresolution time-frequency tiling directly.

Ask the AI about this model

The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.

Related live simulations

Frequently asked questions

Is this wavelet transform multiresolution tool really free?
Yes. Wavelet Transform runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.