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.

翻译：本文首次提出了一种面向融合离散时间信号的以噪声为中心的异常预测方法。通过小波包变换（WPT）实现时频展开，利用正交投影分离信号中的结构成分与残差。高阶统计量（HOS），特别是三阶累积量（及其双谱解释），用于量化提取残差中的非高斯性与非线性耦合特性。通过构建紧凑的噪声特征，并结合经解析校准的马氏距离检测器，得到一种闭式决策规则，该规则在均值偏移假设下服从非中心卡方分布性能。文中通过命题与证明，确立了正交性、能量守恒性、累积量的高斯零行为以及由此导出的检验统计量性质。