Title : Prince transform: a wave-mechanical framework for real-time EEG analysis and early seizure prediction using chirp and drift detection
Abstract:
Standard EEG analysis relies on the Fourier Transform, which assumes additive superposition of stationary sinusoids on the Gaussian complex plane and derives energy post-hoc via Parseval’s theorem. This approach struggles with the multiplicative, non-stationary, and energetically physical nature of neural oscillations.
We derive the Prince Transform directly from de Broglie’s relation λp = h using multiplicative superposition on the Euler Complex Plane. The transform simultaneously extracts spatial wavelength structure, temporal frequency content, and physical energy from EEG signals via the natural logarithm. Its temporal derivative naturally yields two key signatures of homeostatic breakdown: chirp (instantaneous frequency change dω/dτ) and drift (accumulated frequency shift).
These quantities emerge as the coupled response between the linear propagation and nonlinear self-binding terms in the Prince Wave Equation. In pre-ictal states, sustained chirp and systematic drift appear minutes before classical seizure patterns, providing a physically grounded early warning criterion (∂ωT /∂t · t > ωT ). The framework also enables natural, energy-based color mapping for intuitive clinical visualization.
When integrated with machine learning models, the Prince Transform supplies physics-informed features that enhance early seizure detection, artifact rejection, and differentiation of true pre-ictal dynamics. This represents a shift from purely statistical pattern recognition to a wave-ontological understanding of brain activity, with strong potential for real-time implementation in epilepsy monitoring and neurocritical care.
Keywords: Prince Transform, EEG, chirp, drift, seizure prediction, wave ontology, physicsinformed AI
