This is an introduction course to random analysis at graduate level which helps to build the theoretical foundation for students in communication, signal processing and networking areas. Topics include probability and random variables; random processes and sequences; linear system response to random input; special classes of random processes; applications to signal detection and linear minimum mean square error filtering.
Review of Probability and Random Variables
Random Processes and Sequences
Linear Systems Response to Random Inputs
Special Classes of Random Processes (Gaussian, ARMA model, Markov and Poisson)
Applications in Signal Detection
Linear MMSE Filtering (Linear MMSE, Kalman Filter, Wiener Filter)
Linear system theory and random signal theory at undergraduate level. (Although these materials will be reviewed at beginning of the course, we will proceed quickly to graduate level topics.)
Professor Roy You
Email: you@adm.njit.edu
Phone: (973) 596-3528
Office: 333 ECE Building
Office Hour: Monday 4-6pm
Random Signals: Detection, Estimation and Data Analysis
K. Shanmugan and A. Breipohl
John Wiley & Sons, Inc. 1988.
There will be weekly problem sets (20% of grade), one midterm (40%), and one final exam (40%). Some of the problem sets will involve Matlab simulation. You can obtain a copy of Matlab software from the campus computing facility.
|
Week |
Date |
Plan |
Reading |
Homework | |
| 1 | Sept. 7 | Probability, Random Variables | Chp. 2.1, 2.2, 2.3, 2.4 | HW01 | Solution |
| 2 | Sept. 14 | Random Vector, Function of Random Variables | Chp. 2.5, 2.6 | HW02 | Solution |
| 3 | Sept. 21 | Random Process, Stationarity | Chp. 3.1, 3.2, 3.3, 3.5 | HW03 | Solution |
| 4 | Sept. 28 | Random Processes, Correlation, Spectral Density | Chp. 3.4, 3.6 | HW04 | Solution |
| 5 | Oct. 5 | Linear System Response to Random Input | Chp. 4.1, 4.2, 4.3 | HW05 | Solution |
| 6 | Oct. 12 | Gaussian Random Process and Noise | Chp. 5.1, 5.5 | HW06 | Solution |
| 7 | Oct. 19 | K-L Expansion, Sampling, Quantization | Chp. 3.9, 3.10 | ||
| 8 | Oct. 26 | Midterm | |||
| 9 | Nov. 2 | Special Classes of Random Processes | Chp. 5.2, 5.3, 5.4 | HW07 | Solution |
| 10 | Nov. 9 | Binary Detection (MAP) | Chp. 6.1, 6.2 | HW08 | Solution |
| 11 | Nov. 16 | Binary Detection (Bayes, N-P) | Chp. 6.3, 6.4, 6.5 | HW09 | Solution |
| 12 | Nov. 23 | Class Cancelled | |||
| 13 | Nov. 30 | Linear MMSE | Chp. 7.1, 7.2 | HW10 | Solution |
| 14 | Dec. 7 | Bayes MMSE, Innovation | Chp. 7.2, 7.3 | ||
| 15 | Dec. 14 | Final | |||