## OMA356 Syllabus - Random Processes - 2021 Regulation - Open Elective | Anna University

OMA356

RANDOM PROCESSES

L T P C

3003

OBJECTIVES:
• To introduce the basic concepts of probability, one and two dimensional random variables with applications to engineering which can describe real life phenomenon.
• To understand the basic concepts of random processes which are widely used in communication networks.
• To acquaint with specialized random processes which are apt for modelling the real time scenario.
• To understand the concept of correlation and spectral densities.
• To understand the significance of linear systems with random inputs.

UNIT I

RANDOM VARIABLES

9

Discrete and continuous random variables – Moments – Moment generating functions – Joint Distribution- Covariance and Correlation – Transformation of a random variable.

UNIT II

RANDOM PROCESSES

9

Classification – Characterization – Cross correlation and Cross covariance functions - Stationary Random Processes – Markov process - Markov chain.

UNIT III

SPECIAL RANDOM PROCESSES

9

Bernoulli Process – Gaussian Process - Poisson process – Random telegraph process.

UNIT IV

CORRELATION AND SPECTRAL DENSITIES

9

Auto correlation functions – Cross correlation functions – Properties – Power spectral density – Cross spectral density – Properties.

UNIT V

LINEAR SYSTEMS WITH RANDOM INPUTS

9

Linear time invariant system – System transfer function – Linear systems with random inputs – Auto correlation and cross correlation functions of input and output.

TOTAL: 45 PERIODS

OUTCOMES: Upon successful completion of the course, students should be able to
• Understand the basic concepts of one and two dimensional random variables and apply in engineering applications.
• Apply the concept random processes in engineering disciplines.
• Understand and apply the concept of correlation and spectral densities.
• Get an exposure of various distribution functions and help in acquiring skills in handling situations involving more than one variable.
• Analyze the response of random inputs to linear time invariant systems.

TEXT BOOKS:
1. Ibe, O.C.," Fundamentals of Applied Probability and Random Processes ", 1st Indian Reprint, Elsevier, 2007.
2. Peebles, P.Z., "Probability, Random Variables and Random Signal Principles ", Tata McGraw Hill, 4th Edition, New Delhi, 2002.

REFERENCES:
1. Cooper. G.R., McGillem. C.D., "Probabilistic Methods of Signal and System Analysis", Oxford University Press, New Delhi, 3rd Indian Edition, 2012.
2. Hwei Hsu, "Schaum’s Outline of Theory and Problems of Probability, Random Variables and Random Processes ", Tata McGraw Hill Edition, New Delhi, 2004.
3. Miller. S.L. and Childers. D.G., “Probability and Random Processes with Applications to Signal Processing and Communications ", Academic Press, 2004.
4. Stark. H. and Woods. J.W., “Probability and Random Processes with Applications to Signal Processing ", Pearson Education, Asia, 3rd Edition, 2002.
5. Yates. R.D. and Goodman. D.J., “Probability and Stochastic Processes", Wiley India Pvt. Ltd., Bangalore, 2nd Edition, 2012.