Course

Unit 1

Random Processes introduction, Classification statistical properties examples Stationary processes SSS/WSS processes, Examples on SSS/WSS processes Properties of autocorrelation function problems, Examples on WSS/Variance.

Unit 2

Point process -Poisson process concepts properties Mean-autocorrelation of Poisson Process proof Theorems on Poisson Process Problems on Poisson process Gaussian Process- First and Second Order Process Properties – Problems.

Unit 3

The spectrum estimation concepts Mean ergodic theorem, Sufficient condition for Mean ergodicity – Problems Correlation Ergodicity Problems Power spectral density (PSD) concepts- properties, Weiner Kinchine theorem Problems on PSD.

Unit 4

Markov Process Chain concepts, Chapman Kolmogorov theorem, steady state, Classification of states probabilities Problems on Markov chain.

Text Books / References

Text Books:

1. A. Papoulis, and Unnikrishna Pillai, “Probability, Random Variables and Stochastic Processes”, Fourth Edition, McGraw Hill, 2002.
2. J. Ravichandran, “Probability and Random Processes for Engineers”, 1st Edition, IK International, 2015.

Books for Reference:

1. Sheldon M. Ross, “Stochastic Processes”, 2ndEdition, Wiley, 1995.
2. J. Medhi, “Stochastic Processes”, 2nd Edition, New Age International Private limited, 2006.
3. Roy D. Yates, David J. Goodman. (2005). Probability and Stochastic Processes, A Friendly Introduction for Electrical and Computer Engineers. John Wiley

This course introduces the fundamentals of random processes, including their classification, statistical properties, stationary processes (SSS/WSS), autocorrelation, and key models such as Poisson and Gaussian processes. It also covers ergodicity, spectral analysis using power spectral density and the WienerKhinchin theorem, and Markov processes with the ChapmanKolmogorov theorem, focusing on problem-solving and data science applications

Course Outcomes: After successful completion of the course, students will be able to:

• CO1: To gain knowledge about the basics of random process concepts and properties
• CO2: To learn the application of random processes in terms of statistical distributions
• CO3: To gain knowledge about the concepts of spectrum estimation and power spectral density
• CO4: To learn Markovian property and Markov chains and their applications

CO-PO Mapping