# Discrete wavelet transform
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## Microsims — p5.js
### Discrete wavelet transform (p5.js) · `DWT`
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<iframe src="https://editor.p5js.org/sciencenibber/full/hrDBEuz2q" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Discrete wavelet transform — p5.js microsim"></iframe>
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*Decompose a signal into shifted, scaled wavelets for multi-resolution — coarse trends and fine detail at once.*
**Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/hrDBEuz2q) · movement *II · Transforms & the frequency domain* · library `p5js`
### Related microsims
Live sims on neighbouring articles — 6 of them inside this article's own Wikipedia link tree:
- [[Convolution]] *(in tree)*
- [[Data_compression]] *(in tree)*
- [[Discrete_cosine_transform]] *(in tree)*
- [[Fast_Fourier_transform]] *(in tree)*
- [[Functional_analysis]] *(in tree)*
- [[Image_compression]] *(in tree)*
*Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*
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## Links (Wikipedia order)
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`Academic_Press` · `Alfréd_Haar` · `Big_O_notation` · `Binary_tree` · `Binomial_QMF` · `Blob_detection` · `C_(programming_language)` · [[Convolution]] · `DFT_matrix` · [[Data_compression]] · `Daubechies_wavelet` · `Digital_watermarking` · `Discrete_Fourier_transform` · [[Discrete_cosine_transform]] · [[Fast_Fourier_transform]] · `Fast_wavelet_transform` · `Filter_bank` · `Fourier_transform` · [[Functional_analysis]] · `Gaussian_noise` · `Geometric_series` · `Haar_wavelet` · `High-pass_filter` · `ITU-T` · [[Image_compression]] · [[Impulse_response]] · `Ingrid_Daubechies` · `Interlacing_(bitmaps)` · `JPEG_2000` · `JPEG_XS` · `Java_(programming_language)` · `Low-pass_filter` · `Numerical_analysis` · `Pixelation` · `Quadrature_mirror_filter` · [[Recurrence_relation]] · `Ringing_(signal)` · `Scale_parameter` · `Set_partitioning_in_hierarchical_trees` · [[Signal-to-noise_ratio]] · `Sinc_function` · `Stationary_wavelet_transform` · [[Time_domain]] · `Ultra-wideband` · `Video_Coding_Experts_Group` · `Wavelet` · `Wavelet_transform`
> Signal Processing concept · part of the Signal Processing Portal · movement II · !31 変換 henkan.svg
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*Rendered from the live microsim (▶ motion).*
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## See it next
[](Wavelet_transform)
*→ Wavelet transform*
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---
Back to Signal Processing Portal · the room · Semiotic gateway
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## What it is
The discrete wavelet transform decomposes a signal into coefficients localized in both time and scale (frequency) by projecting it onto shifted and dilated copies of a mother wavelet.
## How it works / why it matters
In practice it is implemented as an iterated filter bank: the signal is passed through paired low-pass and high-pass filters and downsampled at each level, producing approximation and detail coefficients across a dyadic (octave) set of scales. This multiresolution analysis captures transient and localized features far better than the Fourier transform and underlies wavelet-based compression such as JPEG 2000 and denoising.
## Signs & universals
Instantiates: transformation, signal, frequency.
## Related
See Wavelet transform, [[Discrete_cosine_transform]], Short-time Fourier transform, Time-frequency analysis, Fourier transform, and Digital filter.
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## From the Real GENERATIVE library
> In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time). ([Wikipedia](https://en.wikipedia.org/wiki/Discrete_wavelet_transform))
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*Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*
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## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Discrete_wavelet_transform) : [Wikitube](https://en.wikitube.io/wiki/Discrete_wavelet_transform)
## Previous hub tags
Tree parent: [[Information_theory]].
Legacy hubs: none.
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*Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*