Levinson Algorithm Implementation for Power Spectrum Estimation

This document presents our course project implementation of the Levinson algorithm for power spectrum estimation. The Levinson algorithm serves as an efficient method for signal analysis and information extraction from time series data. In this project, we have implemented the complete Levinson algorithm with proper code structure, including key functions for autocorrelation calculation, recursive solution of Yule-Walker equations, and spectrum computation. The implementation follows the mathematical formulation where we solve for the prediction error filter coefficients using the recursive Levinson-Durbin procedure, which efficiently computes the solution with O(n^2) complexity rather than the O(n^3) required by direct matrix inversion methods. Our comprehensive experimental documentation provides detailed insights into the algorithm's implementation specifics and practical applications. The document thoroughly covers the algorithm's background theory and fundamental principles, supported by extensive experimental data and result analysis to help readers better understand the algorithm's performance characteristics and advantages. We also discuss certain limitations of the Levinson algorithm, potential improvement directions such as incorporating stability checks during recursion and handling ill-conditioned covariance matrices, along with future application scenarios in signal processing and spectral analysis. Ultimately, this document aims to provide readers with a comprehensive and in-depth understanding of the Levinson algorithm while offering valuable references and guidance for related research and applications in the field.