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lib/filters/cheby1/Cheby1.md
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# CHEBY1: Chebyshev Type I Lowpass Filter
# CHEBY1: Chebyshev Type I Lowpass Filter
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Filter |
| **Inputs** | Source (close) |
| **Parameters** | `period`, `ripple` (default 1.0) |
| **Outputs** | Single series (Cheby1) |
| **Output range** | Tracks input |
| **Warmup** | `period` bars |
### TL;DR
- The Chebyshev Type I filter minimizes the error between the idealized and the actual filter characteristic over the range of the passband, but with...
- Parameterized by `period`, `ripple` (default 1.0).
- Output range: Tracks input.
- Requires `period` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
The Chebyshev Type I filter minimizes the error between the idealized and the actual filter characteristic over the range of the passband, but with ripples in the passband. This type of filter has a steeper rolloff and more passband ripple (type I) or stopband ripple (type II) than Butterworth filters.