Least Squares Estimation of ARMA Model Parameters with Harmonic Recovery Simulation

In "Modern Signal Processing," the simulation program for estimating AutoRegressive Moving Average (ARMA) model parameters using the least squares method and performing harmonic recovery is particularly insightful. This simulation enables deeper understanding of the ARMA parameter estimation process and the principles behind harmonic signal recovery. The implementation typically involves constructing the ARMA model equation Y(n) = -∑a_iY(n-i) + ∑b_jW(n-j) + W(n), where W(n) represents white noise. The core algorithm converts this into a linear regression problem Y = Xθ + ε, with θ containing the AR and MA parameters to be estimated. The least squares solution θ = (X^TX)^{-1}X^TY provides optimal parameter estimates. For harmonic recovery, the program implements spectral estimation techniques like the modified covariance method or Burg's algorithm to extract frequency components from the estimated ARMA model. Key MATLAB functions involved include arma() for model identification, aryule() for autocorrelation computation, and pmusic() for spectral analysis. The simulation visually demonstrates how estimated parameters affect signal reconstruction accuracy and spectral peak detection, making it valuable for both educational and research applications in signal processing.