Lectures

Class Schedule for Spring 2017

 

Week Topic HW (Due Thursdays)
1
1/9
Class organization.
Probability: random variables and random vectors, expected values, characteristic functions.
Random processes: Definitions
Tuesday, Thursday
2
1/16
Random processes: Second-order description (mean, correlation function, power spectrum).
Linear vector spaces: inner products, norms, Hilbert spaces, separability.
Tuesday, Thursday
PS I: 2.3, 2.4, 2.8, 2.10, 2.11
3
1/23
Vector space for random processes: inner product, Karhunen-Loève expansion.
Optimization theory: constrained and unconstrained problems.
Estimation theory: notions of error.
Tuesday, Thursday
PS II: 2.17, 2.19, 2.35, 2.47
4
1/30
Estimation theory: parameter estimation, minimum mean-squared error estimation, MAP estimation, linear estimators and the Orthogonality Principle, maximum likelihood estimation, Cramér-Rao bound.
Tuesday, Tuesday audio backup, Thursday
PS III: 2.14, 2.16, 3.1, 4.1
5
2/6
Estimation theory: The Cramér-Rao bound.
Poisson processes and estimating their characteristics.
Tuesday, Thursday
Spring Recess
6
2/13
Linear and nonlinear waveform parameter estimates. Linear signal estimation: Wiener filters.
Tuesday, Thursday
PS IV: 4.2, 4.3, 4.9, 4.11, 4.14
7
2/20
Linear signal estimation: Wiener filters, adaptive filters.
Tuesday, Thursday
PS V: 4.8, 4.12, 4.16, 4.23
8
2/27
Linear signal estimation: Kalman filters. General signal estimation: Bayesian filtering.
Tuesday (missing some audio), (backup audio); Thursday
Quiz I Due
9
3/6
Estimation theory: spectral estimation.
Filtering in the context of basis expansions: Denoising, wavelets, compressive sensing.
Detection theory: likelihood ratio test.
Tuesday, Thursday
PS VI: 4.31, 4.36, 4.38, 4.41
10
3/13
Spring Break
11
3/20
Detection theory: ROC curves, Neymann-Pearson detection, Stein’s lemma.
Tuesday, Thursday
12
3/27
Distance measures for densities; M models, null-hypothesis testing.
Tuesday
PS VII: 4.44, 4.46, 4.54, 5.1
13
4/3
Detection theory: Sequential detection.
Uncertainties in models;, simultaneous estimation and detection.
Tuesday, Thursday
PS VIII: 5.2, 5.4, 5.6, 5.10, 5.13
14
4/10
Detection theory: Signals in additive noise.
Signal and noise unknowns.
Tuesday, Thursday
PS IX: 5.5, 5.23, 5.27, 5.51
15
4/17
Detection theory: Non-Gaussian detection theory. Type-based detection.
Tuesday, Thursday
Quiz II Due