MATLAB Source Code for Modulus Maxima Detection Algorithm

This MATLAB source code implements a modulus maxima detection algorithm for analyzing time series data. The method identifies singularity points in signals by detecting local maxima in wavelet transform modulus across multiple scales. Through wavelet multiresolution analysis, the program locates modulus maxima points where signal derivatives exhibit discontinuities, which correspond to singularities in the original time series. The algorithm works by first performing continuous wavelet transform on the input signal, then computing the modulus of transformed coefficients. Key functions include wavelet coefficient calculation, modulus computation, and maxima detection through threshold-based peak identification. By analyzing the distribution and propagation patterns of these modulus maxima across different scales, users can distinguish between genuine signal singularities and noise artifacts. This implementation provides a robust framework for signal reconstruction using singularity information. The inverse reconstruction process leverages the detected maxima points to recover essential signal characteristics while filtering out noise components. The MATLAB code includes customizable parameters for wavelet selection, scale ranges, and threshold settings, making it adaptable to various signal processing applications such as fault detection in mechanical systems, biomedical signal analysis, and financial time series examination. The modulus maxima approach offers significant advantages in singularity detection accuracy compared to traditional methods, with applications spanning signal denoising, feature extraction, and transient detection. The provided source code includes comprehensive documentation, example datasets, and visualization functions to facilitate practical implementation and result interpretation.