Brief review of matrix algebra: Linear Least Squares probelm, SVD, condition number. Brief review of stationary random processes: Definitions of Power Spectral Density (PSD) Properties of PSD. Estimation of PSD from finite data: Nonparametric methods: - Periodogram+ Properties, Bias and Variance analysis - BT method, Window design considerations + Time-Bandwidth Product and Resolution-variance tradeoffs in window design - Modified Periodogram methods: Bartlett, Welch. Parametric methods for Rational Spectra: - Covariance properties of AR, MA, ARMA processes - Yule-Walker method, Levinson-Durbin algorithm - Multivariate ARMA processes: State-space representation, subspace parameter estimation. Parametric methods for line spectra (sinusoids in noise) -Models of sinusoids in noise - Higher-order YW method, Pisarenko, MUSIC, ESPRIT, Prony methods. Formulation of the Spatial spectrum problem. Introduction to Higher-Order Spectra.