Custom Linear Prediction Coefficients Algorithm Implementation

This MATLAB-implemented program calculates linear prediction coefficients through the following operational steps: The program utilizes the autocorrelation method of linear prediction coding (LPC) where the algorithm computes coefficients by minimizing the sum of squared differences between actual and predicted values. The core implementation involves solving the Yule-Walker equations through Levinson-Durbin recursion for efficient computation. To utilize this program: 1. Launch MATLAB software and load the program file into the workspace 2. Input your time-series data vector or signal sequence as the required input parameter 3. Execute the main function which handles matrix operations for the normal equations and returns the LPC coefficients Linear prediction coefficients represent fundamental statistical parameters widely used in signal processing for predicting future values in data sequences. The program employs the least squares estimation method, which ensures computational accuracy and numerical stability by minimizing the prediction error variance. The algorithm automatically handles the covariance matrix computation and implements efficient linear system solving through MATLAB's built-in matrix operations. Key algorithm features include: - Automatic order selection based on signal characteristics - Pre-processing for signal normalization - Error handling for ill-conditioned matrices - Efficient memory management for large datasets This implementation provides researchers and engineers with a reliable tool for LPC analysis in applications such as speech processing, financial forecasting, and biomedical signal analysis.