Course Description

ECE 1330: Noise and Stochastic Processes The primary objective of this course is to provide students with a basic understanding of random models and their importance in engineering applications. Many practical systems could not be developed without understanding the impact and degree of uncertainty in the system's input(s) and response. Hence, it is crucial for students to gain both an appreciation for the role of random processes, and, an understanding of the techniques used to model them. A partial list of topics in Electrical Engineering that rely heavily on random models include: Communications Systems, Digital Communications, Wireless Communications, Communications Networks and Signal Processing. This course is intended to provide students with the tools to apply random models in each of the aforementioned disciplines. This course introduces probability and random variables in order to characterize signals in the presence of noise---topics covered include: conceptual and axiomatic definitions of probability, discrete and continuous random variables, the probability density function (PDF), the cumulative distribution function (CDF), and the probability mass function (PMF), expectation and other functions of random variables, conditional probability and independence, Markov and Chebyshev inequalities, multiple random variables, introduction to random processes, correlation, covariance and stationarity. Time permiting, students are introduced the Fourier Transform and its application with respect to Power Spectral Density---leading to the concept of white and colored noise, power spectrum estimation and signal detection.

FYIs and Comments on Recent Classes:

Practice Exam Questions The final exam shall concentrate on chapters 3 and 4, with some 2 and 6; as one way to help prepare I have identified a set of 10 'self-test' problems from the text that cover a range of problems that are consistent with the topics and level of difficulty for the exam. Please note that to answer the chapter-6 problems you will need to read my notes on the Gaussian Process, Autocovariance and Autocorrelation. The former is currently downloadable, the later will be available tonight. I shall also identify (here) the key sections from the book that I recommend you concentrate on. Remember--the problems here represent a practice final and they are drawn from the 'self-test' problems at the end of each chapter: solutions are also in the book. You should also be able to answer any question from the midterm (per the available solutions). The final exam shall consist of five (5) problems. If you did the homeworks, understand the solutions to the midterm and entrance quiz, understand the marginal distribution, understand the random pahsor problem the jointly Gaussian rv, and the Gaussion rp, and can do this self-test you will be in excellent shape for the final exam! I suggest studying first and then attempting the self-test with minimal use of the book and your notes. Self-Test Problems: 2.4, 2.5, 3.3, 3.5, 3.7, 4.2, 4.3, 4.5, 6.3 and 6.4; Additional Suggestions: I have spent considerable effort to create special notes on a number of important topics. These are available for download (above) and you should be comfortable with these topics, namely, statistical independence, counting problems or Bernoulli trials, the computation of expectation and the Gaussian random process. In addition, I spent a great deal of class time discussing the conceptual and computational aspects of variance and its relationship to the moments of a random variable. For the case of jointly distributed random variables these concepts were extended to covariance, correlation and the correlation coefficient. These concepts, the relationships amoung them and their computation should be well understood. Important example problems from class that covered a range of concepts and methods include the sum of a large number of uniformly distributed random phasors, the oscilliscope selection problem from the homework and the random needle dropping experiment and how it could be used to estimated the value of pi. Notes to be posted shall show (for those who could not remain on Friday) the extension of covariance and correlation to autocovariance and autocorrelation in a stochastic process. The concept is the same; however we are concerned with the 'self' (auto means self) covariance and correlation between different instances, or random variables taken at different times, from the same stochastic process. Understand covariance and you understand autocovariance, etc.. Book Sections: Here I reference some sections from chapters 3, 4 and 6 that are of particular importance and I recommend you review. However, this is not exhaustive, for example I do not include the various distribution functions---let the homework problems be you more definitive guide. These are descending order by chapter: 6.1; 6.2; 6.3; 6.9 (my lecture notes are far better); 4.1; 4.2; 4.3; 4.4; 4.5; 4.6; 4.7; 3.2; 3.3; 3.5; 3.7. Other Notes of Interest: A list of trig identities will be provided for you in the event that they may be needed. Also, I will provide the Standard Normal table. Other than that you may bring the course text book, your notes and homeworks, (unfortunately I will not have the graded HW #5 or #6 until Monday---hence you need to rely on my solutions), and anything you can download from this web site. I strongly suggest that you read my lecture notes on the Gaussian Process and the Autocorrelation/Autocovariance.

Honors Project Deadline I just realized that I am going to be in D.C. at NSF on Mon and Tue, hence, I am not able to 'grade' projects that are not turned in by Friday. If you cannot turn in by Friday and *need* a letter grade please let me know, otherwise, I will submit an 'I' and make the changes when I get all the projects---don't push this out long!! The best thing would be to get me the projects by the first week of the new quarter.

Missing Homework Grades Please read this section to see if I am missing any of your work: I am missing homework grades on one or more assignments (from 1-4) from the following students: J. Baranoski (4); J. Buckman (1,2); S. Cooper (2,3); K. Costa (2); D. Goncalves (4); B. Krey (3); There are a few graded assignments outside my door, however, none of these are among them. If you either have one of these graded assignments, or, you know you handed it in but never received it back please contact me via email before Friday. I shall check with the TA to find out if he has any assignments that he has not returned to me (other than the last two). Everyone else is up-to-date.

INSTRUCTOR CONTACT INFORMATION:  

TEACHING ASSISTANT/GRADER:  

TEXT BOOKS:  

Required Text (One):

X. Rong Li, "Probability, Random Signals and Statistics", CRC Press, 1999.

Additional References (FYI):

Yannis Viniotos, "Probability and Random Processes for Electrical Engineers", McGraw-Hill, 1998.
Alberto Leon-Garcia, "Probability and Random Processes for Electrical Engineers", Addison Wesley, Second Edition, 1998.
Robert Hogg and J. Ledolter, "Applied Statistics for Engineers and Pysical Scientists", Macmillan, Second Edition, 1992.
Sheldon Ross, "Introduction to Probability Models", Academic Press, Inc., Fifth Edition 1993, Sixth Edition.
James Higgins and Sallie Keller-McNulty, "Concepts in Probability and Stochastic Modeling", Duxbury Press, 1995.
Leonard Kleinrock, "Queueing System Volume 1: Theory", Wiley Interscience, 1975 (The Classic Text on Queueing Theory).


Supplementary Material (FYI):