FFT/spectral Analysis

What is FFT/spectral Analysis?

Spectral analysis asks how much of a series' variance lives at each frequency. The discrete Fourier transform rewrites a window of data as a sum of sinusoids; the FFT (fast Fourier transform) is the efficient algorithm that computes it, and the resulting power spectrum shows which cycle periods carry the most energy. The Goertzel algorithm, a common alternative in trading tools, evaluates single frequency bins instead, which is cheaper when scanning a short list of candidate periods rather than the whole spectrum.

Raw price breaks the transform's assumptions: it is nonstationary and trend-dominated, so energy floods the lowest frequencies and spectral leakage smears the peaks. Practical use means detrending first (typically a high-pass or roofing filter), analyzing short windows, and reading the spectrum as an estimate for that window only. Ehlers-school practitioners often prefer the autocorrelation periodogram for exactly this reason, but Fourier analysis remains the reference frame for dominant cycle measurement.

How traders use it

• To estimate the dominant cycle period in a lookback window, which then sets adaptive lengths for oscillators and moving averages instead of one fixed setting.
• As a regime read: a sharp, stable spectral peak suggests a tradable cyclic rhythm, while a flat or constantly shifting spectrum argues the market is trending or too noisy for cycle tools.
• As a bandpass building block: once the dominant period is measured, filters can isolate that component and oscillators can be tuned to swing at its rate.