Constructing Orthogonal Wavelet Functions Using B-Spline Functions

There are multiple approaches for constructing orthogonal wavelet functions using B-spline functions. Beyond utilizing cubic (3rd-order) and quartic (4th-order) B-splines, orthogonal wavelets can also be constructed using B-spline functions of different orders. In terms of implementation, while MATLAB provides robust numerical computation capabilities through its Signal Processing Toolbox and wavelet analysis functions like wavedec and waverec, alternative programming languages such as Python (using PyWavelets or SciPy) or specialized mathematical software can also be employed. The construction algorithm typically involves solving refinement equations and applying orthogonalization procedures to B-spline bases. By leveraging different B-spline orders and implementation methodologies, various types of orthogonal wavelet functions can be generated to meet specific requirements across diverse application domains including signal processing, image compression, and numerical analysis.