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Miha Kralj
2026-03-13 13:47:10 -07:00
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lib/numerics/dwt/Dwt.md
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| **PineScript** | [dwt.pine](dwt.pine) |
- The Discrete Wavelet Transform decomposes a price series into multi-resolution frequency components using the a trous (with holes) stationary Haar ...
- Parameterized by `levels` (default 4), `output` (default 0).
- Output range: Varies (see docs).
- Requires `bufferSize` bars of warmup before first valid output (IsHot = true).
- **Similar:** [CWT](../cwt/Cwt.md), [FFT](../fft/Fft.md) | **Trading note:** Discrete Wavelet Transform; decomposes signal into frequency bands at different scales.
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
The Discrete Wavelet Transform decomposes a price series into multi-resolution frequency components using the a trous (with holes) stationary Haar wavelet. Unlike decimated DWT, the stationary variant preserves time alignment at every scale, producing an approximation (trend) and detail coefficients (noise/cycles) at each decomposition level. Each level doubles the effective receptive field: level $L$ captures structure at $2^L$ bars. With 1-8 levels and $O(L)$ per-bar cost, DWT provides a complete multi-scale decomposition that cleanly separates trend from noise without the phase distortion inherent in moving-average cascades.
@@ -111,4 +109,4 @@ First decomposition level fully SIMD. Deeper levels become too small for effecti
- Daubechies, I. "Ten Lectures on Wavelets." SIAM, 1992.
- Holschneider, M. et al. "A Real-Time Algorithm for Signal Analysis with the Help of the Wavelet Transform." Wavelets: Time-Frequency Methods and Phase Space, 1989.
- Percival, D. & Walden, A. "Wavelet Methods for Time Series Analysis." Cambridge University Press, 2000.
- Gencay, R., Selcuk, F. & Whitcher, B. "An Introduction to Wavelets and Other Filtering Methods in Finance and Economics." Academic Press, 2002.
- Gencay, R., Selcuk, F. & Whitcher, B. "An Introduction to Wavelets and Other Filtering Methods in Finance and Economics." Academic Press, 2002.