MATLAB Implementation of Wavelet Transform for Weak Signal Extraction

This MATLAB program implements wavelet transform-based weak signal extraction. The algorithm begins by selecting appropriate wavelet bases (such as Daubechies, Symlets, or Coiflets) to decompose the loaded signal using MATLAB's wavedec function, which performs multi-level wavelet decomposition. The decomposition process separates the signal into approximation and detail coefficients across multiple resolution levels.

Following decomposition, threshold processing is applied to the wavelet coefficients using thresholding functions like wthresh or wden, which help eliminate noise while preserving weak signal components. Different thresholding strategies (hard or soft thresholding) and threshold selection rules (universal, minimax, or SURE) can be implemented based on the signal characteristics.

After threshold processing, signal reconstruction is performed using the waverec function, which reconstructs the signal from the modified wavelet coefficients. The reconstruction process effectively extracts the weak signal components while suppressing noise and interference. This implementation is designed to enhance weak signal processing capabilities, improving the accuracy and reliability of signal analysis through MATLAB's comprehensive wavelet processing functions.