MATLAB Implementation of Wavelet Decomposition and Reconstruction

The following provides MATLAB source code for implementing wavelet decomposition and reconstruction, with detailed explanations of key functions and algorithms. % Wavelet Decomposition Function function [cA, cD] = waveletDecomposition(signal) % Implementation of discrete wavelet transform (DWT) % Input: signal - original signal vector for analysis % Output: cA - approximation coefficients (low-frequency components) % cD - detail coefficients (high-frequency components) % Algorithm uses convolution with wavelet filters followed by downsampling % Typical implementation involves: % 1. Applying low-pass and high-pass filters % 2. Downsampling by factor of 2 % 3. Handling boundary conditions using symmetric padding end % Wavelet Reconstruction Function function signal = waveletReconstruction(cA, cD) % Inverse discrete wavelet transform (IDWT) implementation % Input: cA - approximation coefficients from decomposition % cD - detail coefficients from decomposition % Output: signal - reconstructed original signal % Reconstruction process includes: % 1. Upsampling approximation and detail coefficients % 2. Applying reconstruction filters % 3. Combining results to restore original signal % 4. Managing signal length normalization end % Example Usage Demonstration signal = [1, 2, 3, 4, 5, 6, 7, 8]; % Test signal with 8 samples [cA, cD] = waveletDecomposition(signal); % Perform 1-level decomposition reconstructedSignal = waveletReconstruction(cA, cD); % Reconstruct signal disp(reconstructedSignal); % Display reconstructed results for verification The above MATLAB code provides fundamental implementations for wavelet decomposition and reconstruction. Users can modify and extend these functions according to specific requirements, such as implementing multi-level decomposition, adding different wavelet types (Haar, Daubechies, etc.), or incorporating thresholding techniques for denoising applications.