phasedefined

Phasedefined is a term used in data analysis and modeling to describe approaches that parameterize processes by their phase rather than by absolute time or spatial coordinates. It is most common in contexts where the system exhibits periodic or quasi-periodic behavior, so that observations can be meaningfully compared when aligned by phase rather than by chronological time.

Formal definition: Given a periodic process with period T, the phase is defined as phi = 2π t / T plus an optional phase offset, taken modulo 2π. A phasedefined representation expresses observable quantities as functions of phi, x = f(phi), instead of as functions of t. In practice, the phase variable can be estimated from data via folding, phase tracking, or phase-unwrapping techniques. Phasedefined models may incorporate phase-dependent parameters, allowing dynamics or statistics to vary with phase while keeping a consistent phase reference.

Advantages include reduced within-cycle dispersion, improved alignment across cycles, and simpler aggregation of multi-cycle data. Limitations arise when the period is not stable, when phase estimation is uncertain, or when non-periodic components dominate the signal.

Applications span astronomy (periodic light curves), neuroscience (oscillatory neural activity), geoscience (seasonal cycles), and communications (phase-locked signaling). Related concepts include phase folding, phase unwrapping, circular statistics, and Fourier-based phase analysis.

Note: phasedefined is a descriptive label used in some disciplines to distinguish phase-centered modeling from time-centered approaches; formal definitions may vary by field or method.