Random Process and Noise
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
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