Course Title: Random Signals and Processes
Type of Course: Optional, Theory
.3 Offered to: EEE
Pre-requisite Course(s): None
Concept of random variables and process is essential for the understanding of electrical engineering systems such as telecommunications, signal, image and video processing, biomedical signal processing, genomic signal processing, power systems, evaluation of reliability of engineering systems, computing and son, and interestingly they also have wide range of applications in other fields for example meteorology, genomics, finance, economics, epidemiology etc. Topics include: basics of probability, random variables and their properties and transformations for single and joint densities, moments and characteristic functions, conditional densities and expectations, Inequalities, evaluation of reliability of engineering systems, Central Limit Theorem, estimation of parameters for statistical models, random processes and their stationarity and ergodicity, spectral estimation and input-output relation of LTI systems.
To introduce basic concepts of random variables and processes and develop a solid background as well as the ability to design, analyze and interpret electrical engineering systems and also, apply it in similar systems in other areas in a stochastic setting.
To give a foundation for future courses such as Digital Signal Processing II , Wireless Communications, Radar and Satellite Communication, Introduction to Digital Image Processing, Information and Coding Theory, Introduction to Medical Imaging, Speech Communication, Wireless and Mobile Networks and Power System Reliability.
Provides an essential background for postgraduate study and research in communication and signal processing and interdisciplinary areas.
Fundamental understanding in Calculus, Statistics, Linear Signals and Systems and Signal Processing.
| CO No. | CO Statement | Corresponding PO(s)* | Domains and Taxonomy level(s) | Delivery Method(s) and Activity(-ies) | Assessment Tool(s) |
|---|---|---|---|---|---|
| CO1 | Recall the basics of probability, employ the concept of Bernouli trials to estimate outcomes repeated experiments and evaluation of the reliability of electrical engineering systems | PO(a), PO(b) | C2 C4 |
Lectures, Tutorials, Homeworks | Assignment, Class test, Final exam |
| CO2 | Recognize uni-variate and bi-variate random variables, analyze their properties and perform transformations of uni- and bi-variate random variables and interpret the outcomes | PO(a), PO(b) | C2 C4 |
Lectures, Tutorials, Homeworks | Assignment, Class test, Final exam |
| CO3 | Estimate the moments of uni-rand bi-random variables, and employ to obtain bounds (inequalities) with applications and interpret the outcomes | PO(a), PO(b) | C2 C3 C4 |
Lectures, Tutorials, Homeworks | Assignment, Class test, Final exam |
| CO4 | Identify random processes and analyze their properties including interpretation and estimation of stationarity and ergodicity | PO(a), PO(b) | C2 C4 |
Lectures, Tutorials, Homeworks | Assignment, Class test, Final exam |
| CO5 | Analyze and interpret the output and input-output relation of electrical engineering systems for given random inputs; perform statistical modeling of electrical engineering signals and systems and estimate relevant parameters. | PO(a), PO(b) | C2 C3 C4 |
Lectures, Tutorials, Homeworks | Assignment, Class test, Final exam |
Cognitive Domain Taxonomy Levels: C1 – Knowledge, C2 – Comprehension, C3 – Application, C4 – Analysis, C5 – Synthesis, C6 – Evaluation, Affective Domain Taxonomy Levels: A1: Receive; A2: Respond; A3: Value (demonstrate); A4: Organize; A5: Characterize; Psychomotor Domain Taxonomy Levels: P1: Perception; P2: Set; P3: Guided Response; P4: Mechanism; P5: Complex Overt Response; P6: Adaptation; P7: Organization
Program Outcomes (PO): PO(a) Engineering Knowledge, PO(b) Problem Analysis, PO(c) Design/development Solution, PO(d) Investigation,
PO(e) Modern tool usage, PO(f) The Engineer and Society, PO(g) Environment and sustainability, PO(h) Ethics, PO(i) Individual work and team work,
PO(j). Communication, PO(k) Project management and finance, PO(l) Life-long Learning
* For details of program outcome (PO) statements, please see the departmental website or course curriculum
| K1 | K2 | K3 | K4 | K5 | K6 | K7 | K8 | P1 | P2 | P3 | P4 | P5 | P6 | P7 | A1 | A2 | A3 | A4 | A5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Week | Lectures | Topic | Textbook | COs |
|---|---|---|---|---|
| 1 | 1-3 | Introduction: Overall aspects of the course and its applications, Review of Sample space, set theory, probability measure, Axioms of probability, joint probability, conditional probability, total probability, Bayes theorem, Independence | Chapter 1 | CO1 |
| 2 | 4-6 | Repeated Trials: Bernouli Trials, Laplace-DeMoivre and Poisson approximations, Weak and Strong Law of Large numbers | Chapter 2 and 4 | CO1 |
| 3-4 | 7-12 | Random Variable: Continuous and discrete random variables, transformation method for single random variable, probability density function (pdf) and cumulative density function (CDF), probability mass function (pmf), commonly used pdfs/pmfs, and CDFs | Chapter 3 | CO2 |
| 5 | 13-15 | Moments: Expectation, Variance, and characteristic function, applications of moments and characteristic functions, Inequalities, Reliability applications | Chapters 3-6 | CO1 CO3 |
| 6-7 | 16-21 | Two Random Variables: Joint pdfs and CDFs, joint pmfs, independence and uncorrelatedness, Bivariate Gaussian pdf, Transformation methods for: (i) Two Functions of Two Random Variables, (ii) One Function of Two Random Variables, (iii) method of auxiliary variable, | Chapters 7-9 | CO2 |
| 8-9 | 22-27 | Moments: Joint Moments and Joint Characteristic Functions and applications, Central Limit Theorem, Conditional Density Functions and Conditional Expected Values, hypothesis testing | Chapters 10-11 | CO3 |
| 10-11 | 28-33 | Random Process: continuous and discrete random process, Gaussian, Poisson and Markov Process, Stationarity and Ergodicity, correlation and covariance, wide-sense stationary (WSS) process: (i) properties, (ii) verification of ergodicity, existence of continuity, derivative and integral, process measurements | Chapters 14 and 15 | CO4 |
| 12-13 | 34-39 | Analysis of systems: Spectral Estimation. Correlation and power spectrum. Cross spectral densities. Response of linear systems to random inputs, noise models, statistical parameter estimation techniques | Chapter 18 | CO5 |
Class Participation: Class participation and attendance will be recorded in every class.
Continuous Assessment: Continuous assessment any of the activities such as quizzes, assignment, presentation, etc. The scheme of the continuous assessment for the course will be declared on the first day of classes.
Final Examination: A comprehensive term final examination will be held at the end of the Term following the guideline of the Academic Council.
Class Participation 10%
Continuous Assessment 20%
Final Examination 70%
Total 100%
Probability, Random Variables and Stochastic Processes, Fourth Edition, by Athanasios Papoulis and S. Unnikrishna Pillai, McGraw-Hill.
Probability, Random Variables and Random Signal Principles, Peyton Peebles, Tata McGraw-Hill, 4th edition, 2012.
Fundamentals of Applied Probability and Random Processes, Oliver C. Ibe, Elsevier, 2014.
Probability, Statistics and Random Processes for Electrical Engineering, Alberto Leon Garcia, Pearson Publishers, 2008.