A New Approach to High-Order Electroencephalogram Phase Analysis Details the Mathematical Mechanisms of Central Nervous System Impulse Encoding

Abstract

This paper presents a new electroencephalogram (EEG) analysis technique which is applied to example EEGs pertaining to nine human subjects and a broad spectrum of clinical scenarios. While focusing on technique physical efficacy, the paper also paves the way for future clinically-focused studies with revelations of several quantified and detailed findings in relation to high-order central nervous system communicative impulse encoding akin to a sophisticated form of phase-shift keying. The fact that fine encoding details are extracted with confidence from a seemingly modest EEG set supports the paper’s position that vast amounts of accessible information currently goes unrecognised by conventional EEG analysis. The technique commences with high resolution Fourier analysis being twice applied to an EEG, providing newly-identified harmonics. Except for deep sleep where harmonic phase, φ, behaviour becomes highly linear, φ transitional values, ∆φ, measured between harmonics of progressively increasing order are found to cluster rather than follow a normal distribution (e.g., χ2 = 303, df = 12, p < 0.001). Clustering is categorised into ten Families for which many separations between ∆φ values are writable in terms of k = j/4 or j/3 (j = 1, 2, 3 ...), with a preference for k = j/2 (χ2 = 77, df = 1, p < 0.001), amounts of a Family-specific quantum increment value, α∆φ. A parabolic relationship (r > 0.9999, p < 0.001) exists between α∆φ (and the parabola minimum associates with an additional inter-Family or universal quantum increment value, αmin). Ratios of α∆φ typically align within ± 0.5% of simple common fractions (95% CI).