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Wavelet-Packet-based Noise Signatures With Higher-Order Statistics for Anomaly Prediction
arXiv:2512.12528v1 Announce Type: cross
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.
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.
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