{"ID":2829222,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.12528","arxiv_id":"2512.12528","title":"Wavelet-Packet-based Noise Signatures With Higher-Order Statistics for Anomaly Prediction","abstract":"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.","short_abstract":"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 cumula...","url_abs":"https://arxiv.org/abs/2512.12528","url_pdf":"https://arxiv.org/pdf/2512.12528v1","authors":"[\"Indrakshi Dey\",\"Ilias Cherkaoui\",\"Mohamed Khalafalla Hassan\"]","published":"2025-12-14T02:49:16Z","proceeding":"eess.SP","tasks":"[\"eess.SP\",\"cs.IT\"]","methods":"[]","has_code":false}