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lib/numerics/dwt/Dwt.md
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# DWT: Discrete Wavelet Transform
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Numeric |
| **Inputs** | Source (close) |
| **Parameters** | `levels` (default 4), `output` (default 0) |
| **Outputs** | Single series (Dwt) |
| **Output range** | Varies (see docs) |
| **Warmup** | `bufferSize` bars |
### TL;DR
- 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).
- 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.
## Historical Context