2025/12/14 by Indrakshi Dey, Ilias Cherkaoui, Dey, Indrakshi +3
Computer Science · Engineering · #Anomaly Detection Techniques and Applications #FOS: Computer and information sciences #FOS: Electrical engineering #Fault Detection and Control Systems #Information Theory (cs.IT) #Machine Fault Diagnosis Techniques #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2512.12528
openalex publication_date 2025/12/14 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28
This note develops the first-ever noise-centric anomaly prediction method for a fused discrete-time signal. A Wavelet Packet Transform (WPT) provides a time--frequency expansion in which structure and residual can be separated via orthogonal projection. Higher-Order Statistics (HOS), particularly the third-order cumulant (and its bispectral interpretation), quantify non-Gaussianity and nonlinear coupling in the extracted residual. Compact noise signatures are constructed and an analytically calibrated Mahalanobis detector yields a closed-form decision rule with non-central chi-square performance under mean-shift alternatives. Propositions and proofs establish orthonormality, energy preservation, Gaussian-null behavior of cumulants, and the resulting test statistics.