Least Squares - ARMA Algorithm for Spectrum Analysis

This MATLAB code implements the Least Squares - ARMA (AutoRegressive Moving Average) algorithm, a fundamental method for spectrum analysis. The algorithm is particularly relevant in advanced Digital Signal Processing courses where students learn to analyze frequency components of signals. Spectral analysis serves as a crucial technique for investigating signal frequency characteristics and distribution patterns. The Least Squares - ARMA approach operates by fitting an ARMA model to the input signal through parameter estimation using least squares optimization. The implementation typically involves several key steps: first estimating the AR parameters using covariance methods, then solving for MA parameters through innovation filtering. The spectral density is subsequently derived from the estimated model parameters using the transfer function approach. In MATLAB, this algorithm can be implemented using functions like arma for model estimation and pyulear for spectral calculation. The code generally includes signal preprocessing, model order selection criteria (such as Akaike Information Criterion), parameter estimation routines, and spectral visualization components. The implementation allows researchers and engineers to estimate power spectral density with improved resolution compared to traditional periodogram methods, making it particularly valuable for analyzing signals with mixed spectral characteristics. The MATLAB environment provides excellent support for this algorithm through its Signal Processing Toolbox, enabling efficient computation of autocorrelation functions, matrix operations for normal equations, and spectral plotting capabilities. Proper implementation includes validation techniques to ensure model stability and spectral accuracy.