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Miha Kralj
2026-03-13 13:47:10 -07:00
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lib/numerics/fft/Fft.md
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| **PineScript** | [fft.pine](fft.pine) |
- The FFT indicator computes the dominant cycle period in a price series using a radix-2 Cooley-Tukey Fast Fourier Transform with a Hanning window.
- Parameterized by `windowSize` (default 64), `minPeriod` (default 4), `maxPeriod` (default 32).
- Output range: [minPeriod, maxPeriod] bars.
- Requires windowSize bars of warmup before first valid output (IsHot = true).
- True $O(N \log N)$ radix-2 FFT with bit-reversal permutation and Cooley-Tukey butterflies.
- **Similar:** [IFFT](../ifft/Ifft.md), [CWT](../cwt/Cwt.md) | **Trading note:** Fast Fourier Transform; identifies dominant frequencies/cycles in price data. Foundation of spectral analysis.
The FFT indicator computes the dominant cycle period in a price series using a true radix-2 Cooley-Tukey Fast Fourier Transform with a Hanning window. Rather than outputting frequency-domain magnitudes, it returns the estimated dominant cycle period in bars, making it directly usable as an adaptive period input for other indicators. The implementation uses an in-place iterative radix-2 FFT with bit-reversal permutation and Cooley-Tukey butterfly operations, achieving $O(N \log N)$ complexity. Parabolic interpolation on the magnitude spectrum provides sub-bin frequency resolution. With window sizes restricted to powers of two (32, 64, or 128), the indicator achieves precise cycle detection within user-specified period bounds with pre-allocated work arrays for zero-allocation streaming.
@@ -157,4 +155,4 @@ Moderate SIMD potential: butterfly FMA operations are vectorizable within each s
- Ehlers, J.F. "Rocket Science for Traders." Wiley, 2001.
- Harris, F.J. "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform." *Proc. IEEE*, 1978.
- Oppenheim, A.V. & Schafer, R.W. "Discrete-Time Signal Processing." 3rd edition, Pearson, 2010.
- PineScript reference: [`fft.pine`](fft.pine)
- PineScript reference: [`fft.pine`](fft.pine)