Autumn 2018

**Course No.**

**:**ECE 704 T

**Instructor**

Shahid M Shah, email id: FIRST NAME AT ece.iisc.ernet.in, FIRST NAME DOT nit AT gmail.com

**Credits**

4

**Location**

AB-VI-101

**Lecture Hours**

**Announcement:**

**Course Syllabus**

**UNIT I**

Probability, Random variables & Operations on Random Variables: Introduction to Probability: Probability introduced through sets; joint and conditional probability independence: Bernoulli’s Trials. The Random variable concept: distribution Function: Expectation of a Random Variable: Moments/Transformations of a Random variable.

**UNIT II**

Multiple Random Variables: Vector Random Variables: joint distribution and its properties: Conditional Distribution and Density: Statistical Independence; expected value of a function of a Random variable; Distribution and Density of a sum of Random Variables.

**UNIT III**

Random Processes: Random process concept: Stationarity and Independence: (First order stationary processes, second order and wide sense stationarity, Time Averages and Ergodicity): correlation function: Auto correction Function: Cross –correlation Function & covariance: Measurement of correlation Functions: Gaussian random processes: Poisons Random Process: Probability Density Function/joint probability Density.

**UNIT IV**

Spectral Characteristics of Random Process: Power Density Spectrum and its properties: Relationship between power spectrum and Auto correlation Function: Cross power Density Spectrum and its properties: some Noise definitions. UNIT V Some Practical Applications of the Theory: Linear Systems Fundamental, Random Signal Response of Linear systems, spectrum Characteristics of a system Response, Noise Bandwidth, Noise sources. Information Theory: Entropy and Mutual information for discrete ensembles: Asymptotic equipatition property: Shannon’s Noiseless Coding Theorem. Discrete memory Channels, Shannon’s Noisy Coding, Noise in analog and digital modulation schemes

**Prerequisites**

Basic Set Theory, Mathematical maturity, working brain!

**Course Grade**

T.B.D

**Homeworks**

**References**

TEXT BOOKS:

**1) P.Z Peebles, Probability Random Variables and Random Signal Principles,4/e McGraw Hill,2000 2) Principles of Communication system by Herbert Taub and Donald L. Schilling, 2/e Tata McGraw Hill Publishing, Click to download first part**

1) A popoulis and S.U.Pilai, Probability, Random Variables and Stochastic Processes,4/e,McGraw Hill 2002

REFERRENCE BOOKS:

**Schedule**

- Lecture 1 : Motivation for the course
- Lecture 2: Revision of Set theory, introduction to probability by examples
- Lecture 3: Axioms of Probability, Probability space
- Lecture 4: Frequency based appraoch, Conditional probability