Functions for Computing Continuous Wavelet Transform

This document introduces functions designed for computing continuous wavelet transform (CWT), encompassing both continuous wavelet decomposition and reconstruction operations. These functions serve as essential mathematical tools with broad applications across multiple domains, including image processing, signal analysis, data compression, audio signal processing, and medical imaging. The implementation typically involves mother wavelet selection, scale parameterization, and convolution operations with input signals. Key algorithmic considerations include proper handling of boundary conditions and optimization of computational efficiency through techniques like fast convolution. Understanding these functions provides significant benefits for both professional work and academic research. In subsequent learning modules, we will delve deeper into the operational principles of these functions and demonstrate their practical application for analyzing and processing diverse data types through code examples and parameter configuration guidelines.