Signal Singularity Detection Using MATLAB Wavelet Toolbox

This implementation utilizes MATLAB's wavelet analysis toolbox to detect singular points in signals. The process involves applying continuous wavelet transform (CWT) or discrete wavelet transform (DWT) to analyze frequency and amplitude variations, identifying potential singularities through modulus maxima detection in wavelet coefficients. Key functions like cwt(), wavedec(), and wmaxlev() are employed for multi-scale decomposition, while thresholding techniques help distinguish genuine singularities from noise. This wavelet-based approach enables precise localization of abrupt changes and discontinuities in signal patterns. Such analysis finds applications across multiple domains including signal processing, fault detection in mechanical systems, biomedical signal analysis, and anomaly detection in time-series data. The implementation typically includes steps for wavelet selection, decomposition level optimization, and singularity identification using Lipschitz exponent calculations.