RANDOM SIGNALS and NOISE (EHN 334)
Classroom, hours:
Online, on Fridays between 14:30-17:30
Instructor:
M. Ertuğrul Çelebi, Ph.D., Prof.
E-Mail: mecelebi@itu.edu.tr
Url: http://web.itu.edu.tr/~mecelebi/
Prerequisites:
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:
% 50 Midterms, %10 Homework, %40 Final,
Attendance to at least eight 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,
[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:
March 05 Probability: Basic concepts, counting techniques, conditional probability.
March 12 Repeated trials, random variables, probability density function, important random variables.
March 19 Functions of random variables, expectation, Chebyshev inequality.
March 26 Multidimensional (vector) random variables, conditional distributions.
April 02 Midterm1, Transformations over random variables.
April 09 Sums of random variables, Central limit theorem, Laws of large numbers.
April 16 Definitions of random processes, statistical properties, mean, correlation functions.
April 30 Examples of discrete-time random processes, sum process, binomial counting process.
May 07 Examples of continuous-time random processes, Poisson processes, Brownian motion.
May 21 Midterm II, Stationary random processes, white noise.
May 28 Power spectral density, response of linear systems to random signals.
June 04 Periodogram, optimum linear systems, Wiener filters,
June 11 Markov chains.