Wavelet-Packet-based Noise Signatures With Higher-Order Statistics for Anomaly Prediction

TL;DR

This paper introduces a novel noise-based anomaly prediction method using Wavelet Packet Transform and Higher-Order Statistics to detect non-Gaussian residuals in fused signals, providing a statistically rigorous detection framework.

Contribution

It is the first to develop a noise-centric anomaly prediction approach combining wavelet packet analysis with higher-order statistics for fused signals.

Findings

Effective separation of structure and residual via WPT

Analytically calibrated Mahalanobis detector with chi-square performance

Proven orthonormality and energy preservation properties

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.