Construction of B-Spline Wavelets and Singularity Detection Using Wavelet Transform Modulus Maxima

This article presents the MATLAB implementation of B-spline wavelet construction and singularity detection using wavelet transform modulus maxima. B-spline wavelets serve as fundamental wavelet basis functions that effectively extract both frequency-domain and time-domain characteristics from signals through wavelet transformation. The article provides a detailed explanation of the construction principles and algorithms for B-spline wavelets, accompanied by specific implementation steps in MATLAB code. Key MATLAB functions such as wavelet construction algorithms and modulus maxima calculation methods are demonstrated with practical implementation approaches. Additionally, the article introduces the singularity detection methodology based on wavelet transform modulus maxima, which efficiently identifies abnormal points and abrupt changes in signals. By integrating B-spline wavelets with singularity detection techniques, enhanced performance can be achieved in various signal processing applications. The implementation covers critical aspects including wavelet filter design, multi-resolution analysis, and edge detection algorithms through modulus maxima tracking. Readers are invited to explore this article to gain comprehensive insights into B-spline wavelet theory and its practical applications in singularity detection.