Introduction: The spectral estimation problem and its applications---classical and model-based approaches---issues in spectral estimation.

Review of Probability, Statistics and Random Processes: Random process characterization---bias and variance---ergodicity.

Classical Spectral Estimation: Periodogram---averaged periodogram---Blackman-Tukey spectral estimator---bias/variance trade-off.

Parametric Modelling: Rational transfer function models---model parameter relationships to the auto-correlation---examples of AR, MA, and ARMA processes---issues in model fitting.

Autoregressive Spectral Estimation: Properties of AR processes: connection to linear prediction and the minimum-phase property---Levinson-Durbin recursion---lattice filter representation---implied ACF extension---connection to maximum entropy spectral estimation---MLE of AR parameters---statistics of the MLE---spectral flatness measure and the effects of noise on the AR spectral estimator---AR spectral estimation algorithms (auto-correlation, covariance, modified covariance, and Burg)---model order selection.

Moving Average Spectral Estimation: The MA spectral estimator---MLE estimation: Durbin's method---statistics of the MA parameter estimates.

Autoregressive Moving Average Spectral Estimation: Maximum-likelihood estimation---statistics of the ML estimates---ARMA spectral estimation mthods (Akaike approximate MLE, modified Yule-Walker equations, least-squares modified Yule-Walker equations).

Minimum Variance Spectral Estimation: Filtering interpretation of the periodogram---introduction to BLUE---the minimum-variance spectral estimator---comparison of MVSE and AR spectral estimators (statistical properties, resolution, and implied ACF extension).

Sinusoidal Parameter Estimation: MLE of one sinusoid---extension to the multiple sinusoid case---eigenvector analysis of the covariance matrix---Pisarenko Harmonic Decomposition---principal component method---Kumaresan-Tufts method---MUSIC---approximate MLE methods---iterative filtering algorithm.