RANDOM SIGNALS and NOISE (EHN 334)

 

Classroom, hours:

1303, on Wednesday's between 13:30-16:30

 

Instructor:

M. Ertuğrul Çelebi, Ph.D., Prof.

Room:  2420

Phone: (212) 285 3558

E-Mail:  mecelebi@itu.edu.tr

Url:  http://web.itu.edu.tr/~mecelebi/

Office Hours:  Friday afternoons by appointment

 

Prerequisites:

MTH 271 or MAT 271 Probability and Statistics

 

Course Objective:

To obtain a theoretical knowledge and simulation skills for random sequences and stochastic

signals.

 

Content:

Review of probability, moments, Chebyshev inequalities, vector random variables, conditional

distributions, transformations over vector random variables, central-limit theorem, random

sequences, definition of random processes, autocorrelation and cross-correlation functions,

Poisson process, stationary processes, power spectral density, response of linear systems

to stationary inputs, Wiener filter, Markov process.

 

Grading Policy:

% 40 Midterms,  %15 Homework, %45 Final,

Attendance to at least nine lectures is mandatory

 

Textbook:

Alberto Leon-Garcia, Probability  and Random Processes for Electrical Engineering,

Second Ed., 1994, Addison-Wesley

 

Useful Books:

[1] Steven Kay, Intuitive Probability and Random Processes using MATLAB, 2006, Springer

[2] A. Papoulis, S.U. Pillai, Probability, Random Variables and Stochastic Processes,

Fourth Ed., 2002, McGraw Hill

[3] Peyton Z. Peebles Jr., Probability, Random Variables and Random Signal Principles,

McGraw Hill, 4th Ed., 2001

[4] H. Stark, J. Woods, Probability, Statistics, and Random Processes for Engineers,

Fourth Ed., 2011,  Prentice Hall

[5] Alberto Leon-Garcia, Probability, Statistics, and Random Processes for Electrical

Engineering, Third Ed., 2009 Pearson Prentice Hall

 

 

Tentative Time-Table:

Feb.23   Probability: Basic concepts, counting techniques, conditional probability.

Mar.02   Repeated trials, random variables, probability density function.
Mar.09   Important random variables, Functions of random variables, expectation.

Mar.16   Chebyshev inequality, Multidimensional (vector) random variables.
Mar.23   Midterm I
Mar.30   Transformations over random variables, multidimensional Gaussian random variable.
Apr.06   Sums of random variables, Central limit theorem, Laws of large numbers.

Apr.13   Definitions of random processes, statistical properties, mean, correlation functions.

Apr.20   Examples of discrete-time random processes, sum process, binomial counting process.

Apr.27   Examples of continuous-time random processes, Poisson processes, Brownian motion.

May 11   Stationary random processes, white noise, Midterm II.

May 18   Power spectral density, response of linear systems to random signals.

May 25   Periodogram, optimum linear systems, Wiener filters.

June 01   Markov chains.