MATLAB Implementation of Wavelet Transform with Comprehensive Code Examples

Wavelet transform is a powerful mathematical tool extensively used in signal processing and image analysis. It decomposes signals or images into different frequency components while effectively capturing detailed features and characteristics. Originally developed by foreign scholars, wavelet transform has found widespread applications across various technical domains. For MATLAB implementation, developers typically utilize built-in functions like wavedec for wavelet decomposition and waverec for reconstruction. Key parameters include: - Wavelet family selection (e.g., 'db4' for Daubechies wavelets) - Decomposition level specification - Thresholding methods for denoising applications The algorithm workflow generally involves: 1. Signal preprocessing and normalization 2. Multi-level decomposition using wavelet filters 3. Coefficient thresholding for noise reduction 4. Signal reconstruction from modified coefficients Common applications include: - Signal denoising using wdenoise function - Image compression with wavedec2 for 2D signals - Feature extraction through detailed coefficient analysis This implementation demonstrates proper handling of boundary conditions and efficient memory management for large datasets, making it suitable for both educational and professional use cases.