| Class | Topic | Comments |
|---|---|---|
| 8/28 | Class organization Probability spaces, independent events, conditional probability, random variables |
|
| 8/30 | Probability functions, expected values (mean and variance), characteristic functions, random vectors, functions of random variables, correlation, the Gaussian random variable and the Gaussian random vector. | Read Johnson's notes on optimization theory |
| 9/4 | Functions of one random variable, multiple random variables - joint densities, independence, conditional densities/expectations, covariance and correlation matrices, sums of independent random variables | |
| 9/6 | Random processes: definition; mean, correlation, covariance functions; wide-sense stationary; power spectra. | PS #1 due |
| 9/11 | Random processes: white noise, filtering of processes, sampling processes, ergodicity, Karhunen-Loève expansions | |
| 9/13 | Estimation theory: terminology, minimum mean squared error (MMSE) estimators | PS #2 due |
| 9/18 | MMSE estimation | |
| 9/20 | Orthogonality principle, linear MMSE estimation | PS #3 due |
| 9/25 | Other Bayesian estimators: Minimum absolute error and Maximum a posteriori (MAP) estimators |
|
| 9/27 | FIR Wiener filters and predictors Maximum likelihood estimation (MLE): definition, properties |
|
| 10/2 | Cramer-Rao bound | PS #4 due |
| 10/4 | Expectation-Maximization (EM) algorithm |
|
| 10/9 | Expectation-Maximization (EM) algorithm | PS #5 due |
| 10/11 | Likelihood ratio test (Bayes and Neyman-Pearson detection) | Quiz #1 handed out |
| 10/16 | NO CLASS | Mid-term Recess |
| 10/18 | Likelihood ratio test (Bayes and Neyman-Pearson detection) | Quiz #1 due in class |
| 10/23 | ROC curves, M models, composite tests | |
| 10/25 | Detection of signals in Gaussian noise | PS #6 due |
| 10/30 | Detection in the presence of unknowns: random and non-random parameters, generalized likelihood ratio tests (GRLT) | |
| 11/1 | Detection in the presence of unknowns (Gaussian noise) | |
| 11/6 | Detection in the presence of unknowns (Gaussian noise) | PS #7 due |
| 11/8 | Detection in the presence of unknowns (Gaussian noise) | |
| 11/13 | Sequential detection | |
| 11/15 | Stein's lemma | |
| 11/20 | Continuous-time detection | PS #8 due Quiz #2 handed out |
| 11/22 | NO CLASS | Thanksgiving Recess |
| 11/27 | LMS adaptive filters | |
| 11/29 | LMS adaptive filters | Quiz #2 due |
| 12/4 | Kalman filters | |
| 12/6 | Kalman filters | PS #9 due |
| 12/12 | NO CLASS | Final Exam handed out |
| 12/19 | NO CLASS | Final Exam due 5:00 p.m. |