## Signals and Stochastic Process by Mr. V. Rama Krishna Sharma M. Tech, (Ph. D) and Ms. Sangeeta Singh M. Tech, (Ph. D) 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. Code : SSPJHEEE31 Recommended For : JNTU B. Tech EEE 3rd Year 1st Semester

#### After Learning this subject,you should be able to

• 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 16:44:33   units   |   12

• 1:18:48

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 Approximation

• 1:14:23

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 Paley-Wiener criterion for physical realization, Problems on transfer function, Relationship between Bandwidth and Risetime, Convolution & problem

• 1:19:10

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 spectrum

• 1:12:41

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 5

• 0:17:15

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

• 1:14:16

UNIT 3.1
Laplace Transforms: Laplace Transforms, Introduction, Region of Convergence (ROC), Problems, Properties of Laplace transform, Differentiation in s-domain, Integration in Time-domain, Conjugation, Convolution in time domain, Convolution in s-domain, 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 Synthesis

• 1:25:11

UNIT 3.2
Z - Transforms: Z-TRANSFORMS, Discrete time complex exponential, Periodicity of discrete time complex exponential, Introduction To Z- Transforms, Concept of Region Of Convergence (ROC), Properties of Z-Transforms, Properties of Z-Transforms - part 2, Properties of Z-Transforms - part 3, Properties of Z-Transforms - 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, PRE-ReQUISITES I, PRE-REQUISITES 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, PRE-REQUISITES 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 4

• 1:26:24

UNIT 4.1
Random Processes-Temporal 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 Wide-Sense Stationarity, (N-Order) and Strict-Sense Stationarity, Concept of Statistical Independence, Time Averages, Ergodicity, Mean-Ergodic, Correlation Ergodic

• 1:14:40

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 2

• 1:26:21

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, Mean-squared Value of System Response, Autocorrelation Function of Response, Cross-Correlation Of Functions Of Input And Output, Problem 1, Problem 2

• 1:16:18

UNIT 5.1
Random Processes-Spectral 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 Cross-Power Spectrum Density (CPSD)

• 1:01:31

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, Cross-Power Density Spectrums of Input and Output, Autocorrelation function, Cross-Power Spectrum Density