Course Identification

Probability

Fourier analysis

In this course we will cover basic concepts underlying sampling and processing of signals. The course will be roughly divided into two parts where the first part will focus on signal sampling and the second half will focus on the fundamentals of statistical signal processing.

Tentative list of topics:

1. Introduction and Nyquist rate sampling
2. Sampling in shift-invariant subspaces
3. Introduction to compressed sensing
4. Sub-Nyquist sampling of multiband signals
5. Finite rate of innovation sampling
6. Applications to radar and ultrasound
7. Beampatterns and sparse arrays
8. Random variables: Joint and conditional distribution, MSE estimation.
9. Stochastic processes: Stationarity and ergodicity, spectral density.
10. Filtering of random signals: LTI systems and stationarity, sampling of stationary signals.
11. Estimation of random signals: Wiener filtering, adaptive filters.
12. Digital communications on a nutshell: MAP decoding, Viterbi detection.
13. Parameter estimation 1: bias-variance tradeoff, Fisher information.
14. Parameter estimation 2: Cramer-Rao bound, maximum likelihood.

Upon successful completion of this course, the students should understand theoretically and be able to apply signal processing tools in various relevant scenarios, ranging from generic signal acquisition to medical imaging and digital communications.

In additions, the student should be able to adapt these concepts when tackling new unexplored challenges involving the acquisition, processing, and inference of signals.

A. Papoulis, Probability, Random Variables and Stochastic Processes, 3rd Ed., McGraw-
Hill, 1991. 

S. M. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory,
Prentice-Hall, 1993 

H. L. Van Trees, Detection, Estimation and Modulation Theory, Part I, John Wiley & Sons,
1968.

Y. C. Eldar Sampling theory: Beyond Bandlimited Systems. Cambridge University Press, 2015.

Y. C. Eldar, G. Kutyniok, Compressed Sensing: Theory and Applications. Cambridge University Press, 2012.