One-Dimensional Discrete Wavelet Transform

Complete source code for implementing One-Dimensional Discrete Wavelet Transform (DWT) with both decomposition and reconstruction capabilities. The implementation utilizes the db6 (Daubechies 6) wavelet for transformation, providing a balance between smoothness and compact support. Key features include flexible parameterization allowing users to easily modify the mother wavelet and scaling function parameters to achieve different analytical results. The code structure employs MATLAB's Wavelet Toolbox functions including wavedec for decomposition and waverec for reconstruction, with clear variable naming for coefficients (approximation and detail coefficients). The package includes comprehensive MATLAB tutorials demonstrating practical implementation steps: - Signal preprocessing and normalization - Multilevel wavelet decomposition using wavedec function - Coefficient thresholding and manipulation techniques - Perfect reconstruction validation methods - Visualization of approximation and detail coefficients at different decomposition levels The implementation follows standard DWT algorithms with efficient memory management for handling large datasets. Each function includes detailed comments explaining the mathematical operations and parameter significance, making it suitable for both educational and research applications in signal processing and data analysis.