1D Signal Two-Level Wavelet Decomposition and MATLAB Application

1D Signal Two-Level Wavelet Decomposition Overview

1. Two-Level Approximation Decomposition: The original signal is averaged every 4 values to capture the approximate components at this level.

2. Two-Level Detail Decomposition: The difference between every 2 consecutive values in the original signal provides the detailed components at this level.

3. One-Level Detail Decomposition: The difference between the odd and even-indexed values of the original signal is calculated to extract finer details.

4. Signal Recovery: After the decomposition, the signal can be reconstructed by combining the approximations and details from each level.

In MATLAB, you can implement these wavelet decompositions to analyze various signals effectively, applying discrete wavelet transform (DWT) functions for both decomposition and reconstruction steps.