Adaptive Morlet Wavelet Transform Deep Learning Layer

Differentiable parameterized Morlet wavelet transform layer is constructed for adaptive time-frequency representation of complex signals.

Traditional wavelet transform has certain limitations in engineering applications. It heavily relies on experts’ understanding of system dynamic characteristics when selecting key parameters such as mother wavelet basis functions, decomposition levels, and threshold rules. While traditional wavelet analysis is inherently well suited for non-stationary signals, its decomposition process still depends largely on predefined basis functions and manually selected parameters

To address the above limitations, an end-to-end data-driven method embedded with a differentiable parameterized Morlet wavelet transform is constructed based on MATLAB's Deep Learning Toolbox. This deep learning layer fuses the rigorous time–frequency analysis capability of wavelet theory with the nonlinear feature learning advantages of deep neural networks.

The construction of this deep learning layer refers to the paper Adaptive wavelet-enhanced data-driven framework for surface quality prediction in ultra-precision manufacturing.