Ethoryx Spectral analyzes any numerical sequence for periodic structure invisible to standard statistical methods. Lomb-Scargle periodogram in log-space with matched-filter significance testing against shuffled controls. Returns z-scores, peak frequencies, and confidence levels. One API call.
Three-layer pipeline: periodogram, shuffle baseline, z-score output.
Computes spectral power at each target frequency using the Lomb-Scargle method — optimal for unevenly sampled or log-spaced data. Unlike FFT, handles non-uniform sampling natively. Scans up to 2,000 frequency points per call.
The same sequence is randomly shuffled up to 300 times. Each shuffled version is analyzed with the same periodogram. This establishes the null distribution — what spectral power looks like when any structure is destroyed by randomization.
At each frequency, the true spectral power is compared to the shuffled distribution. A z-score above 2.0 means the signal at that frequency is statistically significant — it's real structure, not noise. The API returns all significant peak frequencies and their z-scores.
# Analyze a numerical sequence for hidden periodic structure
curl -X POST "https://api.ethoryx.io/v1/spectral/analyze" \
-H "Content-Type: application/json" \
-d '{"sequence":[0.1,0.3,-0.2,0.5,0.1,-0.4,0.2,0.6,-0.1,0.3,0.2,-0.3,0.4,0.1,-0.2,0.5],"n_freqs":50,"n_shuffles":100}'
# Response
{
"n_significant": 3,
"max_z": 4.21,
"peak_freqs": [2.14, 5.89, 8.33],
"peak_z_scores": [4.21, 3.07, 2.44],
"sequence_length": 16,
"analysis_time_ms": 342.1,
"engine": "Ethoryx Spectral Engine"
}Detect hidden periodicities in financial returns, trading volumes, or volatility series. Standard spectral methods miss structure in log-sampled data. Ethoryx Spectral's log-space periodogram is designed for exactly this type of data. Identify market microstructure, seasonality, and regime-change frequencies.
Network traffic, API call patterns, and system logs produce numerical sequences with characteristic spectral profiles. An intrusion or data exfiltration changes the profile — new frequencies appear, existing ones shift. Ethoryx Spectral detects the shift and tells you which frequency changed, not just that something is different.
Gene expression time series, protein folding trajectories, and neural spike trains all contain periodic structure. Ethoryx Spectral detects these periods with statistical significance testing — no distributional assumptions required. Works with unevenly sampled experimental data natively.
Sensor streams from industrial equipment, environmental monitors, and IoT devices. Detect mechanical resonance, electrical interference, or environmental cycles in any sensor data. The z-score output integrates directly into alerting pipelines — z > 2 triggers an alert.
Requires uniformly sampled data. Returns raw power spectrum with no significance testing. You see peaks but don't know if they're real or noise. No built-in null hypothesis. Sensitive to windowing and zero-padding choices.
Handles non-uniform and log-sampled data natively. Every peak comes with a z-score computed against 300 shuffled controls. You know exactly which peaks are real (z > 2) and which are noise. No windowing artifacts. One API call, interpretable output.
Pro plan ($99/mo) includes full spectral analysis. Sequences up to 500K elements. 300 shuffle controls.
Paste any numerical sequence below. The engine runs a Lomb-Scargle periodogram with 100 shuffled baseline controls and returns z-scores for each significant frequency. A z-score above 2 means the signal is real — not noise.