Page 43 - R2017-REC-ECE-UG Syllabus

Department of ECE, REC

SEMESTER IV

MA 17454 TRANSFORMS AND RANDOM PROCESSES L T P C
3 2 0 4
OBJECTIVE:
• To acquaint the student with Fourier transform techniques used in wide variety of situations.
• To provide the required mathematical support in real life problems and develop probabilistic models
which can be used in several areas of science and engineering.

UNIT I FOURIER TRANSFORMS 15
Statement of Fourier integral theorem – Fourier transform pair – Fourier sine and cosine transforms –
Properties – Transforms of simple functions – Convolution theorem –Parseval’s identity - Application to
boundary value problems.

UNIT II ONE - DIMENSIONAL RANDOM VARIABLE 15
Discrete and continuous random variables – Moments – Moment generating functions – Binomial, Poisson,
Uniform, Exponential, Gamma, Rayleigh, Weibull and Normal distributions – Functions of Random Variable.

UNIT III TWO - DIMENSIONAL RANDOM VARIABLES 15
Joint distributions – Marginal and conditional distributions – Covariance – Correlation and Linear regression
– Transformation of random variables – Applications of Central Limit Theorem.

UNIT IV RANDOM PROCESSES 15
Classification – Stationary process – Markov process - Poisson process and its properties – Random telegraph
process.

UNIT V SPECTRAL DENSITIES AND LINEAR SYSTEMS 15
Auto correlation functions – Cross correlation functions – Power spectral density – Cross spectral density –
Properties-Linear time invariant system – System transfer function – Linear systems with random inputs.

TOTAL= 75 PERIODS
OUTCOMES:
On completion of the course students will be able to
• Develop skills to solve problems using Fourier transform techniques
• Apply the basic concepts of probability, one dimensional and two dimensional Random Variables.
• Apply the concept of correlation and regression in real life situation.
• Analyze signals which evolve with respect to time in a probabilistic manner.
• Develop skills in solving problems on power spectral density function in linear time invariant
systems.

TEXT BOOKS:
1. T.Veerarajan, ‘Probability, Statistics and Random Processes with Queueing Theory and
Queueing Networks’ , Mc Graw Hill, 2016.
2. Peebles. P.Z., "Probability, Random Variables and Random Signal Principles", Tata McGraw-
Hill, 4th Edition, New Delhi, 2002.

Curriculum and Syllabus | B.E. Electronics and Communication Engineering | R2017 Page 43