Course Description:
The course is designed to give the student an introduction to the important subject of random signals and noise. Random signals and processes, play a very important role in the fields of communications, signal processing, and control, as well as in many other fields, as far-fetched as the stock market and biological sciences.
The course will begin with a brief review of probability theory. The random process will then be defined. This will be followed by a discussion of stationary processes, correlation functions and power spectral densities. The effect of linear (and non-linear) operations on random signals will also be discussed. We will define important random processes such as gaussian processes (including white gaussian noise) and bandlimited random processes, and some of their important properties. We will also discuss some practical analysis applications of random processes and noise in different fields, e.g., calculating signal-to-noise ratios in communication systems. If time permits we will also describe Wiener-Hopf filtering and the Kharhunen-Loeve expansion at the end of the course.
Faculty/Manager:
Irving Kalet
Contact Information:
Irving Kalet
email: ik2127@columbia.eduClass Homepage: http://www.columbia.edu/%7Ecv2176/4815_home.htm Credits for Course: 3 Viewing Schedule: 2 lectures per week Prerequisites: SIEO W3658 (Probability) or the equivalent Required Text(s): S. Miller and D. G. Childers, Probability and Random Processes: With Applications to Signal Processing and Communications, Elsevier-Academic Press, 2004 Reference Text(s): S. Haykin, Communications Systems, J. Wiley and Sons, New York, Fourth Edition, 2001
A. Papoulis and S.U. Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill, New York, Third Edition, 1991
A. Papoulis and S.U. Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill, New York, Fourth Edition, 2002
A. H. Haddad, Probabilistic Systems and Random Signals, Pearson-Prentice-Hall, New Jersey, 2006Grading: Final 60%
Midterm 30% (This mark can only help you!!)
Homeworks 10% Required!
* The information contained in this syllabus is subject to change at any time.