A Right-Sided Cl(0,2)-Valued Linear Canonical Stockwell Transform: Rigorous Formulation and Chirp-Adaptive Computation

Quadratic phase disperses the spectrum of chirped multicomponent data and can defeat the ordinary Stockwell analysis. We formulate a right-sided Cl(0,2)-valued linear canonical Stockwell transform (CLCST) on a positive real Hilbert space, using standard Clifford conjugation, a real scalar window, and an invariant multiplication order. Since Cl(0,2) is isomorphic to the quaternion algebra, the construction is algebraically a one-sided quaternion transform; its contribution over existing quaternion Stockwell and quaternion linear canonical Stockwell formulations is not a larger algebra but a rigorously ordered chirp–Clifford Stockwell transform (CST)–dechirp factorization, direct unit-integral-window reconstruction, and a reproducible fast Fourier transform (FFT) realization for chirp estimation. We correct the canonical output-phase ordering and specify the discrete correlation kernel and sign-preserving zero-frequency regularization. A nonsymmetric-window stress test verifies these conventions independently. The theory establishes pointwise boundedness, covariance, reconstruction, and a collapsed-energy identity. Experiments on noisy synthetic fields, a four-component signal, a Shepp–Logan phantom, and measured Hubble image content with an injected phase aberration quantify concentration, resolution, and computational cost. The results delimit rather than conceal the method’s scope: it targets a global quadratic phase in Cl(0,2), while orientation sweeps, zero-mean windows, locally varying chirps, and higher-dimensional Clifford algebras require additional machinery.