8/12/2019 Ece201 Probability Theory and Random Process Th 1.10 Ac29

1/2

ECE201 Probability Theory and Random Processes L T P C3 0 0 3

Version No.: 1.10Prerequisite: ECE206 Signals and SystemsObjectives:

To discuss the concepts of discrete and continuous random variables and to calculate theparameters such as mean and variance. To apply vector space concepts in random signal processing. To classify various types of probability distributions that occurs frequently in communication

and signal processing.

To associate the concept of strong law of large numbers and the role of Central limittheorem in the convergence of the random variables.

To illustrate the concept of random process in WSS and SSS with the importance ofErgodicity and its real time applications.

To estimate the power spectral density for a given random signal.Expected Outcome:1. Obtain probability law (distribution) for a set of output random variables.2. Identify a specific distribution to be used for a particular random data.3. Interpret the concept of convergences in random signals from different applications.4. Describe the random signals in terms of its average properties such as average power in the

random signal and its spectral distribution.

5. Model and analyze the effect of noise in electronic circuits used in communication systems.Unit I Probability & Random variables

Introduction to Probability-Joint and Conditional Probability-Independent Events-CombinedExperiments-Bernouli`s Trial-Random Variables-concepts-Distribution and Density Function-Conditional Distribution and Density function.

Unit II Special distributionsExpectations-Moments (variance)- Uniform Distribution, Gaussian Distribution, BinomialDistribution and Poisson distributions.

Unit III Operations on Random VariableOperations on One Random Variable- MGF-Chernoff`s Inequality & Bounds-Multiple Random

Variables-Vector Random Variables-Joint distribution and its Properties-Joint Density and its

Properties- Central limit theorem- Operation on two random variables expected value of afunction of random -2D Gaussian distribution.

Unit IV Random processRandom process- realizations, sample paths, discrete and continuous time processes.Probabilistic structure of a random process; mean, autocorrelation and autocovariance functionsStationarity- strict-sense stationary (SSS) and wide-sense stationary (WSS) processes.

Autocorrelation function of a real WSS process and its properties, cross-correlation function .Ergodicity and its importance. Spectral representation of a real WSS process- power spectraldensity, properties of power spectral density. Cross-power spectral density and properties.autocorrelation function and power spectral density of a WSS random sequence.

Proceedings of the 29th Academic Council [26.4.2013] 318

8/12/2019 Ece201 Probability Theory and Random Process Th 1.10 Ac29

2/2

Unit V Special Random ProcessessLinear time-invariant system with a WSS process as an input- stationarity of the output, auto-correlation and power-spectral density of the output; examples with white-noise as input-Modeling of noise sources-Resistive Noise Sources-Effective Noise Temperature-Power Gain-

Average Noise figures-Average Noise Temperatures-Model of Example System-Markov Process.

Textbook:1. P.Z. Peebles, Probability, Random Variables and Random Signal Principles, 4th edition,

McGraw Hill, 2000

Reference Books:1. Papoulis and S.U. Pillai, Probability, Random Variables and Stochastic Processes, 4th

Edition, McGraw-Hill, 2002.

2. Sophoncles J. Orfanidis, Optimum Signal processing, McGraw Hill, New York 1990.3. John G. Proakis & Dimitris G. Manolakis Digital Signal Processing, Pearson Education

(Indian adopted version), 1/e, 2006.

4. Seymour Lipschutz, Theory and problems of probability, Schaums outline series, McGrawHill, 1987.

5. Hwei Hsu, Probability, Random variables, Random processes, Schaums outline series,McGraw Hill, 2002.

6. Monson H.Hayes, Statistical digital signal processing and modelling, John Wiley and sons,2002.

7. H. Stark and J.W. Woods, Probability and Random Processes with Applications to SignalProcessing, Prentice Hall 2002.

Mode of Evaluation: CAT- I & II, Quizzes, Assignments/ other tests, Term EndExamination.

Proceedings of the 29th Academic Council [26.4.2013] 319