3 papers
math.ST2026
Probabilistic Analysis of Scalogram Ridges in Signal Processing
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
While ridges in the scalogram, determined by the squared modulus of analytic wavelet transform (AWT), is a widely accepted concept and utilized in nonstationary time series analysi…
math.ST2025
On Random Fields Associated with Analytic Wavelet Transform
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
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 ti…
math.PR2024
Gaussian Approximation for the Moving Averaged Modulus Wavelet Transform and its Variants
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
The moving average of the complex modulus of the analytic wavelet transform provides a robust time-scale representation for signals to small time shifts and deformation. In this wo…