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Miha Kralj
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lib/trends_FIR/sinema/Sinema.md
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| **Signature** | [sinema_signature](sinema_signature.md) |
- The Sine-Weighted Moving Average (SINEMA) applies sine-wave weighting to data points within the lookback window.
- Parameterized by `period`.
- Output range: Tracks input.
- Requires `period` bars of warmup before first valid output (IsHot = true).
- **Similar:** [ALMA](../alma/alma.md), [BLMA](../blma/blma.md) | **Complementary:** Cycle indicators | **Trading note:** Sine-weighted MA; half-sine kernel for naturally smooth bell-shaped weights.
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
The Sine-Weighted Moving Average (SINEMA) applies sine-wave weighting to data points within the lookback window. Weights follow the formula $w_i = \sin(\pi \cdot (i+1) / N)$, creating a smooth bell-shaped distribution that emphasizes middle values while gracefully tapering at the edges. Unlike SMA's uniform weighting or WMA's linear ramp, sine weighting provides a natural transition that reduces high-frequency noise while preserving mid-frequency trends.
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## References
- Harris, F. J. (1978). "On the use of windows for harmonic analysis with the discrete Fourier transform." *Proceedings of the IEEE*, 66(1), 51-83.
- Oppenheim, A. V., & Schafer, R. W. (2010). *Discrete-Time Signal Processing* (3rd ed.). Pearson.
- Oppenheim, A. V., & Schafer, R. W. (2010). *Discrete-Time Signal Processing* (3rd ed.). Pearson.