University of Michigan, Winter 2012

Instructor: Clayton Scott

Classroom: 1017 Dow

Time: TTh 9-10:30

Office: 4433 EECS

Email:

Office hours: Monday 1-3 or by appointment.

__Textbook__: None. I'll distribute my notes.

__Supplemental references__, on reserve at the library:

1) *Fundamentals of Statistical Signal Processing, Volume 1:
Estimation Theory*, Steven Kay, 1993

2) *Fundamentals of Statistical Signal Processing, Volume 2:
Detection Theory*, Steven Kay, 1998

3) *Statistical Signal Processing*, Louis Scharf, 1991

4) *An Introduction to Signal Detection and Estimation*, Vincent
Poor, 2nd ed., 1994

__Topics to be covered__: Theoretical aspects of estimation,
filtering, and detection. Applications of the theory to Fourier and wavelet domain signal
denoising, channel estimation, object tracking, binary communication,
modulation, matched filtering, Rayleigh fading channels, and functional
magnetic resonance imaging. Some applications will be developed in class,
and others through the homeworks.

__Prerequisites__:

EECS 501 or equivalent, linear algebra, signals and systems, familiarity
with MATLAB.

__Lecture notes__:

- Statistical signal processing
- The signal subspace model, orthogonal projections, and least squares estimation
- Eigendecompositions and the spectral theorem
- The multivariate Gaussian distribution
- Sufficient statistics
- Estimation theory
- Minimum variance unbiased estimation
- The Cramer-Rao lower bound
- Rao-Blackwellization
- Maximum likelihood estimation
- Bayesian estimation
- Bayesian estimation in the Gaussian linear model
- Application: Wavelet denoising
- Linear estimation
- Filtering
- Linear prediction
- Wiener filtering
- Kalman filtering
- Application: Channel estimation
- Detection theory
- Bayes risk detection
- Neyman-Pearson detection
- Application: The binary symmetric channel
- Signal detection in Gaussian noise
- Uniformly most powerful tests and the Karlin-Rubin theorem
- Bayes factors and generalized likelihood ratios
- Application: The Rayleigh fading channel
- CFAR detectors
- Additional topics as time permits

__Grading__:

- 45% Homework
- 25% Midterm exam: Wed. Feb. 22, 6-9 PM, GG Brown 1504.
- 30% Final exam: Tue. April 24, 9:30 AM - 12:30 PM, location TBA

__Cancelled lecture__: Feb. 9

__Make-up lecture__: Monday Feb. 6, 5:30 -- 7:00 PM, EECS 1303.

__Homework Policy__

Homeworks are due in the 564 slot in
EECS 2420 by 5 pm on the assigned due date. All homework assignments are
to be
completed on your own. You are allowed to consult with other students in
the current class regarding the conceptualization of the problem and
possible methods of solution, but you may not share details, whether in
the form of scrap work, final writeups, or computer code. All written and
programming work is to be generated by you working alone.
You are not allowed to possess, look at, use, or in anyway derive
advantage from existing solutions that you may come across.

__Honor Code__

All undergraduate and graduate students are expected to abide by the
College of Engineering Honor Code as stated in the Student Handbook and
the Honor Code Pamphlet.

__Students with Disabilities__

Any student with a documented disability needing academic adjustments or
accommodations is requested to speak with me during the first two weeks of
class. All discussions will remain confidential.