Year: 2025
Type: preprint
Abstract: Despite the broad application of the analytic wavelet transform (AWT), a systematic statistical characterization of its magnitude and phase as inhomogeneous random fields on the time-frequency domain when the input is a random process remains underexplored. In this work, we study the magnitude and phase of the AWT as random fields on the time-frequency domain when the observed signal is a deterministic function plus additive stationary Gaussian noise. We derive their marginal and joint distributions, establish concentration inequalities that depend on the signal-to-noise ratio (SNR), and analyze their covariance structures. Based on these results, we derive an upper bound on the probability of incorrectly identifying the time-scale ridge of the clean signal, explore the regularity of scalogram contours, and study the relationship between AWT magnitude and phase. Our findings lay the groundwork for developing rigorous AWT-based algorithms in noisy environments.
Source: arXiv (Cornell University)
Authors: Liu, Gi-Ren, Sheu, Yuan-Chung, Wu, Hau-Tieng
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979249707
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