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Unit - 1 Introduction to Signals & Systems

Unit 1Signals

1.1 Introduction

1.2 Basics of Elementary Signals

1.3 Basic Operations on Signals

1.4 Classification of signals

1.5 Introduction

Unit - 2 Time domain representation of LTI System

Unit 2Time Domain Representation of LTI systems

2.1 Input Output relation

2.2 Definition of the impulse response

2.3 Convolution Sum

2.4 Convolution Integral

2.5 Computation of convolution sum

2.6 Properties of Convolution Sum

2.7 System Interconnections

2.8 System properties in terms of the impulse response step response in terms of the impulse response.

Unit - 3 Fourier Series

Unit 3Fourier Series

3.1 Fourier series representation of periodic CT signals

3.2 Dirichlet condition for the existence of Fourier series

3.3 Orthogonality

3.4 Basic functions

3.5 Amplitude and phase response

3.6 FS representation of CT signals using trigonometric and exponential Fourier series

3.7 Application of Fourier Series

3.8 Properties of Fourier series

3.9 Gibbs Phenomenon

Unit - 4 Fourier Transform

Unit 4Fourier Transform

4.1 Fourier Transform representation of aperiodic CT signals

4.2 Dirichlet condition for the existence of Fourier transform

4.3 Evaluation of magnitude and phase response

4.4 Fourier transform of standard continuoustime signals

4.5 Properties and their significance

4.6 Interplay between time and frequency domain sinc and rectangular signals

4.7 Fourier transform for periodic signals

Unit - 5 Laplace Transform

Unit 5Laplace Transform

5.1 Definition of Laplace Transform

5.2 Limitations of Fourier transform and need of Laplace transform

5.3 ROC

5.4 Laplace transform of standard periodic and aperiodic functions

5.5 Properties of Laplace transform and their significance

5.6 Laplace transform evaluation using properties

5.7 Inverse Laplace Transform based on partial fraction expansion

5.8 Stability consideration in Sdomain

5.9 Application of Laplace transform to LTI system analysis

Unit - 6 Probability and Random Variables

Unit 6Probability and Random Variables

6.1 Experiment Sample space Event

6.2 Probability Conditional Probability and Statistical Independence

6.3 Baye’s theorem

6.4 Uniform and Gaussian Probability models

6.5 Continuous and Discrete random variables

6.6 Cumulative Distributive function Probability density function Properties of CDF and PDF

6.7 Statistical averages mean moments and expectations Standard deviation and variance

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