Detecting Bimodal Spectral Structure in Single-Channel Time Series: A Model-Free Metric with Validation on Meditation EEG

Abstract

Existing time-series analysis methods—power spectral density, wavelet transforms, and stationarity metrics such as coefficient of variation (CV) and sample entropy—characterize signals through band power, peak location, or amplitude variability. These approaches do not quantify whether a signal contains two distinct oscillatory modes separated by a valley within a frequency band of interest. We propose anchor_score, a model-free metric that detects such bimodal structure in a single channel without training data. We validate anchor_score on synthetic signals, on LIGO O1/O4c1 detector data, and on a 24-subject meditation EEG dataset (OpenNeuro ds001787; 12 expert meditators, 12 novices; 256 Hz; 64 EEG channels). The metric is compared against five conventional and baseline measures: theta-band power, coefficient of variation, sample entropy, pairwise coherence, and naive peak counting. Anchor_score achieved a group-level Mann-Whitney p = 0.034, while theta power (p = 0.29), CV (p = 0.41), sample entropy (p = 0.58), pairwise coherence (p = 0.21), and naive peak counting (p = 0.61) did not. Sensitivity analysis showed that the result strengthened after excluding outliers (p = 0.0002), and a permutation test confirmed one extreme subject was unlikely to arise by chance (p = 0.037). Cross-validation across three parameter settings, four frequency bands, three window lengths, and four channel subsets confirmed stability. The method requires only a single-channel time series, produces an interpretable 0-1 score, and is orthogonal to conventional measures. It is applicable to clinical EEG, mechanical vibration monitoring, financial time series, and any domain where bimodal structure carries information. Potential relevance to researchers in the following areas:- EEG analysis, sleep staging, anesthesia monitoring, and neurological disorder detection- Meditation and contemplative neuroscience- Mechanical vibration analysis and industrial fault detection- Time series analysis in finance and economics- Spectral analysis and signal processing methodology- Dynamical systems and coupled oscillator research The metric is model-free, requires no training data, and produces interpretable outputs. A limited version of the implementation is available for peer review upon request; the full implementation is retained as a commercial asset. A companion paper on the underlying theoretical framework is in preparation.