Class Schedule for Spring 2018
Week  Topic  HW (Due Thursdays) 

1 1/8 
Class organization. Probability: random variables and random vectors, expected values, characteristic functions. Random processes: Definitions Tuesday, Thursday 

2 1/15 
Random processes: Secondorder 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 1/22 
Vector space for random processes: inner product, KarhunenLoève 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 1/29 
Estimation theory: parameter estimation, minimum meansquared error estimation, MAP estimation, linear estimators and the Orthogonality Principle, maximum likelihood estimation, CramérRao bound. Tuesday, Tuesday audio backup, Thursday 
PS III: 2.14, 2.16, 3.1, 4.1 
5 2/5 
Estimation theory: The CramérRao bound. Poisson processes and estimating their characteristics. Tuesday, Thursday 
Spring Recess 
6 2/12 
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 2/19 
Linear signal estimation: Wiener filters, adaptive filters. Tuesday, Thursday 
PS V: 4.8, 4.12, 4.16, 4.23 
8 2/26 
Linear signal estimation: Kalman filters. General signal estimation: Bayesian filtering. Tuesday (missing some audio), (backup audio); Thursday 
Quiz I Due 
9 3/5 
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 3/12 
Spring Break  
11 3/19 
Detection theory: ROC curves, NeymannPearson detection, Stein’s lemma. Tuesday, Thursday 

12 3/26 
Distance measures for densities, M models, nullhypothesis testing. Tuesday 
PS VII: 4.44, 4.46, 4.54, 5.1 
13 4/2 
Sequential detection. Uncertainties in models: simultaneous estimation and detection. Tuesday, Thursday 
PS VIII: 5.2, 5.4, 5.6, 5.10, 5.13 
14 4/9 
Detection theory: Signals in additive noise. Signal and noise unknowns. Tuesday, Thursday 
PS IX: 5.5, 5.23, 5.27, 5.51 
15 4/16 
NonGaussian detection theory, typebased detection. Tuesday, Thursday 
Quiz II Due 