Wavelet Transform-Based Signal Singularity Detection and Denoising Routines

In this routine collection, we employ wavelet transforms to detect signal singularities and perform denoising. Wavelet transform is a powerful signal processing technique that decomposes signals into multiple sub-frequency bands, enabling better characterization of signal properties. The implementation involves using wavelet decomposition functions (such as wavedec in MATLAB) to break down signals into detail and approximation coefficients across different scales. Specifically, these routines utilize wavelet transforms to identify singular points in signals through modulus maxima analysis while removing noise using thresholding techniques like soft/hard thresholding applied to wavelet coefficients. This process enhances signal clarity and reliability by preserving important features while suppressing noise components. For detailed implementation specifics including algorithm parameters and function usage, please refer to the program source code which contains commented explanations of the processing steps.