Overview
 Units 12
 Duration 16:44:33
 Branch EEE
 Language English
Course Description
This course gives basic understanding of random process which is essential for random signals and systems encountered in Communications and Signal Processing areas. Stochastic Process gives the basic understanding of random process and its characteristics along with the response of linear time invariant systems.
Recommended For
B.E/ B.Tech Electrical and Electronics Engineering
University
Learning Outcomes
 Understand basics of Signals and Systems required for all Electrical Engineering related courses.
 Understand concepts of Signals and Systems and its analysis using different transform techniques.
 Understand basic understanding of random process which is essential for random signals and systems encountered in Communications and Signal Processing areas.
 Basic understanding of random process and its characteristics along with the response of linear time invariant systems. Further, its study is essential for communication and signal processing areas.
Curriculum


UNIT 1.1 Signal Analysis: Inrtoduction, Standard Signals, Standard Signals & Signal Operations, Signal Operations & Problem, Problems on signals, Analogy between vectors and signals, Orthogonal vector and signal space, Approximation of function by a set of mutually orthogonal functions, Mean Square Error, Closed or Complete Set of Mutually Orthogonal Functions, Orthogonality in Complex Functions, Problem on Signal Approximation1:18:48



UNIT 1.2 Signal Transmission Through LTI System: Signal Transmission Through LTI System, Classification of systems, Example of Linear & Non linear systems, Example 2 Linear & non linear, Time invariant (TIV) and Time variant(TV), Problem for TIV & TV, Causal and non  causal, Stable and unstable systems Part  1, Stable and unstable systems Part  2, Problem for stable and unstable systems, Method to check for stability of a system, Impulse Response, LTI System, Transfer function of an LTI System part 1, Transfer function of an LTI System part 2, Filter characteristics of linear system, Distortionless Transmission, Signal Bandwidth & System Bandwidth, Ideal Filter Characteristics, Ideal LPF, Causality and PaleyWiener criterion for physical realization, Problems on transfer function, Relationship between Bandwidth and Risetime, Convolution & problem1:14:23



UNIT 2 Fourier Series: Fourier Series, Introduction, Representation of Fourier Series, Dirichlet's Conditions, Trignometric Fourier Series  part 1, Trignometric Fourier Series  part 2, Evaluation of fourier coefficients  part 1, Evaluation of fourier coefficients  part 2, Alternate form of Transfer Function System, calculation of fourier coefficients for even and odd functions, Exponential Fourier Series, Relation between TFS and EFS, Properties of fourier series  part 1, Properties of fourier series  part 2, Properties of fourier series  part 3, Complex fourier spectrum1:19:10



UNIT 2.1 Fourier Transforms: Fourier Transforms, Conditions for existence of Fourier Transform, Fourier Transform of standard signals  part 1, Fourier Transform of standard signals  part 2, Fourier Transform of standard signals  part 3, Fourier Transform of standard signals  part 4, Properties of Fourier Transform  part 1, Properties of Fourier Transform  part 2, Properties of Fourier Transform  part 3, Properties of Fourier Transform  part 4, Properties of Fourier Transform  part 51:12:41



UNIT 2.2 Fourier Sampling: Sampling Theorem, Anti Aliasing Filter, Types Of Sampling, Impulse Sampling, Flat Top Sampling, Reconstruction Of Signal from its samples0:17:15



UNIT 3.1 Laplace Transforms: Laplace Transforms, Introduction, Region of Convergence (ROC), Problems, Properties of Laplace transform, Differentiation in sdomain, Integration in Timedomain, Conjugation, Convolution in time domain, Convolution in sdomain, Laplace Transform of useful functions, Relation between Fourier Transform and Laplace Transform, Analysis Of LTI System, Inverse Laplace Transform, Problem, Problem 2, Problem 3, Waveform Synthesis1:14:16



UNIT 3.2 Z  Transforms: ZTRANSFORMS, Discrete time complex exponential, Periodicity of discrete time complex exponential, Introduction To Z Transforms, Concept of Region Of Convergence (ROC), Properties of ZTransforms, Properties of ZTransforms  part 2, Properties of ZTransforms  part 3, Properties of ZTransforms  part 4, Inverse Z  transform  part 1, Inverse Z  transform  part 2, Inverse Z  transform  part 3, Stochastic processes Introduction, Stochastic processes Introduction part 1, Stochastic processes Introduction part 2, PREReQUISITES I, PREREQUISITES FOR STOCHASTIC (RANDOM) PROCESS, What is a Random Variable, What is a Random Variable part 1, Probability distribution Function and Properties of Distribution Function, Expression for distribution function, Plot of distribution Function, Probability Density Function, Numerical Example for density function, PREREQUISITES FOR STOCHASTIC (RANDOM) PROCESS, OPERATIONS ON, Moments, Moments about the Mean Value Part 1, Moments about the Mean Value Part 2, Moments about the Mean Value Part 3, Moments about the Mean Value Part 41:25:11



UNIT 4.1 Random ProcessesTemporal Characteristics: Random processes temporal characteristics, Random Process Concept, Classification of Processes, CRP & DRP & CRS & DRS, Deterministic and Nondeterministic Processes, Distribution and Density Functions, Concept of Stationarity First Order Stationarity, Second Order and WideSense Stationarity, (NOrder) and StrictSense Stationarity, Concept of Statistical Independence, Time Averages, Ergodicity, MeanErgodic, Correlation Ergodic1:26:24



UNIT 4.2 Autocorrelation Function: Autocorrelation Function (ACF), Properties Of ACF Part 1, Properties Of ACF Part 2, Cross Correlation Function (CFF), Properties Of CCF, Covariance Functions part 1, Covariance Functions part 2, Gaussian Random Process part 1, Gaussian Random Process part 21:14:40



UNIT 4.3 Poisson Random Process: Poisson Random Process part 1, Poisson Random Process part 2, Random Signal Part 1, Random Signal Part 2, Mean Value of System Response, Meansquared Value of System Response, Autocorrelation Function of Response, CrossCorrelation Of Functions Of Input And Output, Problem 1, Problem 21:26:21



UNIT 5.1 Random ProcessesSpectral Characteristics: Random Processes, Power Spectrum & its Properties  part 1, Power Spectrum & its Properties  part 2, Properties of PDS part 1, Properties of PDS part 2, Properties of PDS part 3, Properties of PDS part 4, The CrossPower Spectrum Density (CPSD)1:16:18



UNIT 5.2 Properties of CPSD: Properties of CPSD, Relationship between CPSD & CCF part 1, Relationship between CPSD & CCF part 2, Spectral Characteristics of System Response, Power Density Spectrum of Response, CrossPower Density Spectrums of Input and Output, Autocorrelation function, CrossPower Spectrum Density1:01:31

Instructor
Mr. V. Rama Krishna Sharma M. Tech, (Ph. D) and Ms. Sangeeta Singh M. Tech, (Ph. D)
Rama Krishna is currently working as an Associate Professor in the Department of Electronics & Communications Engineering for Sreenidhi Institute of Science & Technology, Ghatkesar, Hyderabad. He has more than a decade of Teaching experience. He holds a Master’s Degree in the specialization of Wireless Communications and also in the pursuit of Doctorate in the area of Communications Engineering. He delivered several guest lectures in reputed Engineering Colleges. He is a Member of International Association of Engineers (Hongkong) and also the Life Member of Indian Society for Technical Education.Sangeeta has more than decade of experience in teaching. She is currently working as Assistant Professor at Vardhaman College of Engineering, Hyderabad. Her areas of interest are Signals, VLSI Digital Logic Design and Analog Communications. She has authored several national and international papers in International Journal of Engineering Research and Technology. Her Submission on “Area and Power Efficient SelfChecking Modulo 2n +1 Multiplier” won accolades at International Journal of Computer Applications.