Wavelet Transform-Based Power Spectrum Estimation

This MATLAB simulation code implements power spectrum estimation using wavelet transform techniques. The implementation includes fundamental wavelet transform principles and the Mallat algorithm for efficient signal decomposition and reconstruction.

The simulation demonstrates wavelet transform as a signal processing technique that decomposes signals into different frequency components. The code implements core wavelet concepts through the Mallat algorithm, which provides efficient multi-resolution analysis using filter banks for decomposition and reconstruction operations. The algorithm implementation includes both forward and inverse transform procedures with proper boundary handling.

Beyond wavelet implementation, the code provides comprehensive comparisons between classical and modern power spectrum estimation methods. Classical methods include Periodogram and Welch's method implementations with proper windowing and averaging techniques. Modern spectrum estimation techniques feature Yule-Walker autoregressive modeling and Maximum Entropy method implementations using prediction error minimization approaches. Each method's performance is evaluated through spectral resolution, variance, and bias analysis.

This MATLAB simulation enables deep understanding of wavelet transform principles and their applications in spectral analysis. The comparative analysis of different power spectrum estimation techniques provides valuable insights into their respective advantages and limitations, supporting advanced research and applications in signal processing and spectral analysis domains.