Implementation of 1D and 2D Wavelet Transforms

This implementation performs 1D and 2D wavelet transforms within the MATLAB environment. The comprehensive wavelet families supported include: - Haar wavelet (simplest orthogonal wavelet basis) - Daubechies wavelets orders 1-6 (db1-db6) with increasing vanishing moments - Symlets orders 1-6 (sym1-sym6) - nearly symmetric wavelets - Coiflets orders 1 and 2 (coif1-coif2) with balanced vanishing moments - Splines and reverse splines for smooth signal representation - CDF 9/7 (Cohen-Daubechies-Feauveau) and Le Gall 5/3 wavelets (commonly used in JPEG2000) - S+P wavelets with filter configurations: (2,2), (4,2), (4,4), (6,2), and (2+2,2) - Two Ten "TT" wavelet design - Low-complexity wavelet designs for efficient computation - HVS (Human Visual System) designed Visual 9/3 wavelet These wavelet families can be implemented using MATLAB's Wavelet Toolbox functions such as wavedec for decomposition and waverec for reconstruction. For 2D transforms, functions like dwt2 and idwt2 handle image processing applications. The wavelets are suitable for various signal processing applications including image compression (using wavelet coefficients thresholding), signal filtering (denoising), and multi-resolution analysis. Through proper selection of wavelet bases and decomposition levels, users can achieve precise and efficient signal processing and analysis.