Course Details

Course details of EE6111
Course NoEE6111
Course TitleSpectral Estimation
Course ContentIntroduction: 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.
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