This preprint introduces a formal diagnostic framework for a class of time-domain signals frequently encountered in tokamak plasma measurements. Signals acquired from magnetic pickup coils, electron cyclotron emission diagnostics, and reflectometry systems often exhibit strong nonstationarity, frequency chirping, intermittency, overlapping modal activity, and approximate scale-invariant spectral structure. While these characteristics are well known empirically, they are commonly analyzed under broad and informal notions of “nonstationary signals,” without a precise characterization of the underlying signal class. To address this gap, the paper defines a class of Geometry-Constrained, Scale-Invariant Nonstationary (GCSIN) signals. The definition makes explicit five structural properties observed in tokamak diagnostics: time-varying frequency content, approximate power-law spectral behavior over finite bands, structured superposition of physically meaningful modes, geometric constraints arising from toroidal confinement, and frequency evolution that is more naturally represented in logarithmic rather than linear frequency coordinates. From this definition, the paper derives representational consequences that are independent of any specific algorithm. In particular, it shows that commonly used linear-frequency time–frequency methods are intrinsically mismatched to GCSIN signals, leading to systematic dispersion and ambiguity that arise from violated structural assumptions rather than from noise or implementation choices. The framework further clarifies why geometry-agnostic representations conflate physically distinct modes when their frequency content overlaps. The scope of the work is strictly diagnostic and representational. No control logic, decision-making systems, real-time enforcement mechanisms, or stabilization strategies are considered or implied. The concept of a “matched representation” is introduced solely to articulate alignment between signal structure and diagnostic kernels, without prescribing a unique transform or claiming optimality. The Toroidal Log-Chirplet Transform is discussed as one illustrative example of a representation aligned with the defined signal class. By formalizing the signal class prior to method selection, this work provides a principled foundation for evaluating existing time–frequency tools, guiding the design of future diagnostic representations, and clarifying the limits of what can be inferred from time–frequency analysis alone in tokamak plasma diagnostics.
Nicolas Brian Quiroz (Wed,) studied this question.