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lib/numerics/cwt/Cwt.md
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# CWT: Continuous Wavelet Transform
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Numeric |
| **Inputs** | Source (close) |
| **Parameters** | `scale` (default 10.0), `omega0` (default 6.0) |
| **Outputs** | Single series (Cwt) |
| **Output range** | Varies (see docs) |
| **Warmup** | 1 bar |
### TL;DR
- CWT computes the magnitude of the Continuous Wavelet Transform at a specified scale using the Morlet wavelet, providing a time-frequency decomposit...
- Parameterized by `scale` (default 10.0), `omega0` (default 6.0).
- Output range: Varies (see docs).
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
CWT computes the magnitude of the Continuous Wavelet Transform at a specified scale using the Morlet wavelet, providing a time-frequency decomposition that measures the energy content of a specific frequency band at each point in time. Unlike Fourier analysis which loses time localization, the wavelet transform maintains both time and frequency information simultaneously. The output is a non-negative magnitude series where peaks indicate strong presence of the target frequency (determined by the scale parameter) and troughs indicate absence of that frequency component.
## Historical Context