EC3500.Res_Fall.FY12 EC3500 – Analysis of Random Signals

Instructor: Monique P. Fargues, Span 456, fargues@nps.edu, *2859, office hours: posted or by appointment Course Goals: This course provides the foundation needed to study and extract information from non-deterministic signals and noise which commonly occur in engineering problems. Topics include properties of random processes, correlation functions, energy and spectral densities, linear systems and mean square estimation, noise models, and introduction to queueing theory (time permitting). Concepts are applied to various scenarios commonly found in today’s electronic systems such as evaluation of sensor data correlation, target distance identification, communication signals detection, transmission channel equalization, etc… Text and References: One textbook is indicated as reference to the course. Unfortunately not one single textbook covers the range of topics discussed within the course. This text is a good reference which will provide you with extensive resources in the concepts area. However, it does not discuss some of the later material covered in the course (specific filters and intro to queueing theory). Note that I teach mostly from my notes (which you need to download) and I refer to the texts/references for proofs or extensions I don’t have time to cover in the classroom. I will use the text for most HW problems. Copy of the second text is also available on reserve at the library (apply to resident students).

Probability and stochastic processes – a friendly introduction for electrical engineers, R. Yates, & D. Goodman, 2nd ed. Wiley, isbn:0-471-27214-0

Probability, random variables, and random signal principles, 4th ed. P. Peebles, 2001, isbn: 0-07-366007-8 Probability, random variables and random processes, 2nd edition, H. Hsu, Scahum’s Outline, 2011 Probability and Random Processes for Electrical and Computer Engineers, J. Gubner, Cambridge Press, 2008. http://www.cs.mcgill.ca/~mcleish/644/normal.html MATLAB tutorials, http://courses.cs.tamu.edu/rgutier/cpsc689_f05/ Mathworks MATLAB tutorials: http://www.mathworks.com/academia/student_center/tutorials/launchpad.html Probability and Statistics for Engineers, 6th ed., Johnson, Prentice-Hall Performance Evaluation of Computer and Communication Systems, J-Y. Le Boudec, EPFL, http://perfeval.epfl.ch/ http://www.itl.nist.gov/div898/handbook/eda

• Course outline: Random Concepts Review

• Concept of probability, event, random variable (RV), Concept & properties of cumulative distribution function (CDF) & probability density function, Conditional probability/ Bayes’ theorem, Mean, moment, skewness, kurtosis, Transformation of Random Variables, Useful random variables pdf specifics, Statistical independence between RVs, IID RVs, Correlation between RVs, correlation coefficient.

• Random vector definition, Random vector statistical description and properties, Relationship between correlation

& covariance matrices, Cross-correlation, cross-covariance matrices: definition & properties, Central limit theorem, Application to signal analysis.

Random Signals/Processes

• Random signal/sequence definition, Signal mean, variance, autocorrelation & autocovariance, normalized cross-correlation, Statistical characterization of random signals (Wide sense stationarity, Correlation & cross-correlation for stationary RPs, Signal average, Ergodicity, Periodicity, Cyclostationarity, etc…).

• Specific examples of RPs: white noise, colored noise, Bernoulli process, Random walk, telegraph signal, counting process, Poisson process, MA process.

• How to estimate correlation lags; biased/unbiased estimator issues. • Frequency domain description for a stationary process: Power spectral density & Cross Power Spectral density.

Random Signals & Linear Systems

Introduction: Properties of random signals obtained as outputs to LTI systems: Mean, cross-correlation between input/output signals, Frequency domain analysis (output PSD and cross PSD expressions for LTI systems).

Matched Filter: Deterministic signal: – continuous / discrete signal cases, Random signal – discrete signal case, applications to radar signal return and communication signals detection.

Wiener Filter: Orthogonality principle, FIR Wiener filtering concepts, examples, applications to channel equalization and noise cancellation, spatial filtering for MIMO environments.

Introduction to Queuing Theory (as time permits) Queueing Systems, birth-death process, Little’s formula, M/M/1, M/M/s and M/M/1/K queues.

• Grades: 2 tests, each worth 25%; assignments: worth 50%. • HWs: A few problems will be assigned when appropriate to apply the various concepts covered in the classroom.

HWs will not be collected; however they constitute an essential part of the learning process for the course. You are responsible for working on the problems as they get assigned to facilitate the understanding of the concepts covered in class. Solutions will be made available.

• Exams:

o Test 1 will be in class closed books/notes. You will be allowed to bring in 2 one-sided (8.5*11") sheets on which you may write whatever you feel may be useful to you. Tables will be provided if needed.

o Test 2 will have a take home portion if it requires the use of MATLAB. Take home section(s) will follow the following protocol: “This is a take-home exam. Open books/notes. You may not discuss this test via any form of communication (written, oral, or computer), or exchange any type of information related to this test with anyone, except the instructor. By turning in your test, you acknowledge having read, agreed to, and followed the above instructions. Violations of this protocol are violations of the Honor Code and will be processed as such.”

• Test schedule: early November, early December. • Class notes: Copies of partially filled-in PowerPoint notes used during classes will be made available electronically in

the SAKAI course account in the folder Resources/NotePacks&Syllabus. Data and other material needed during the course will also be made available in the SAKAI course account. You will receive an e-mail notification when available. You are responsible for printing and bringing class notes to class as needed. I will not have copies available in class.

• Assignments:

o Some of the assignment material is contained in the classnotes (referred to as “Examples”), these will be assigned as they are encountered in the notes and due within one week.

o In addition, MATLAB will be used during the course. You should be familiar with the software before you take this course or will be expected to learn it on your own. MATLAB tutorials can be found online, for example, see references above. A good recommended MATLAB tutorial book is “Mastering MATLAB 7,” by D. Hanselman & B. Littlefield.

o You are encouraged to discuss your work with fellow classmates or the instructor regarding assignments. However, the work turned in (report and/or software implementation) should be your own work only. Data and code from other students are not to be used in reports. Work turned in which is found to violate these guidelines will be considered a violation of the academic honor code (See Section 218 of the student handbook for further details).

o Late reports will not be accepted unless pre-approved by the instructor for special circumstances only. • Academic Honor Code: Students must follow the academic honor code at all times. Work turned in (tests,

assignments, project reports, and all software implementations) should be your own work only.