Wavelet-Packet-based Noise Signatures With Higher-Order Statistics for Anomaly Prediction
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911316837400576 |
|---|---|
| author | Dey, Indrakshi Cherkaoui, Ilias Hassan, Mohamed Khalafalla |
| author_facet | Dey, Indrakshi Cherkaoui, Ilias Hassan, Mohamed Khalafalla |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wavelet-Packet-based Noise Signatures With Higher-Order Statistics for Anomaly Prediction Dey, Indrakshi Cherkaoui, Ilias Hassan, Mohamed Khalafalla Signal Processing Information Theory 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. |
| title | Wavelet-Packet-based Noise Signatures With Higher-Order Statistics for Anomaly Prediction |
| topic | Signal Processing Information Theory |
| url | https://arxiv.org/abs/2512.12528 |