Course Details
Subject {L-T-P / C} : EC2601 : Signals and Systems { 2-1-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Ajit Kumar Sahoo
Syllabus
Module1: Signals and Systems: Continuous-Time and Discrete-Time Signals, Transformations of the Independent Variable, Exponential and Sinusoidal Signals, The Unit Impulse and Unit Step Functions, Basic System Properties. [5 hrs.]
Module2: Linear Time Invariant Systems: Discrete-Time LTI Systems, The Convolution Sum, Continuous-Time LTI Systems, The Convolution Integral, Properties of Linear Time-Invariant Systems, Causal LTI Systems Described by Differential and Difference Equations. [6 hrs.]
Module 3: Fourier representations of signals: Fourier Series Representation of Periodic Signals Fourier Series Representation of Continuous-Time Periodic Signals, Fourier Series Representation of Discrete-Time Periodic Signal, Filtering, Continuous-Time Fourier Transform for aperiodic and Periodic Signals, Systems Characterized by Linear Constant-Coefficient Differential Equations, Discrete-Time Fourier Transform of aperiodic and periodic signals. [15 hrs.]
Module 4: Sampling: Representation of a Continuous-Time Signal by Its Samples, The Sampling Theorem Reconstruction of a Signal from Its Samples Using Interpolation, Aliasing, Discrete-Time Processing of Continuous-Time Signals [4 hrs.]
Module5: The Laplace and Z -Transforms: The Laplace Transform, region of convergence and its properties, Causality and Stability, Determining the Frequency Response from Poles and Zeros. The Z-Transform: The Z-Transform, Properties of Region of Convergence, Properties of the Z-Transform, Inversion of the Z-Transform, Causality and Stability. [6 hrs.]
Course Objectives
- To understand the fundamental characteristics of signals and systems.
- To understand signals and systems in terms of both the time and transform domains, taking advantage of the complementary insights and tools that these different perspectives provide.
- To develop the mathematical skills to solve problems involving convolution, filtering, and sampling.
Course Outcomes
CO1: Able to understand the fundamental characteristics of continuous-time and discrete-time signals and systems. <br />CO2: Able to classify systems based on their properties and determine the response of LTI system using convolution. <br />CO3: Able to analyze the spectral characteristics of continuous-time periodic and aperiodic signals using Fourier analysis. <br />CO4: Able to analyze system properties based on impulse response and Fourier analysis. <br />CO5: Able to understand the process of sampling and the effects of under sampling. <br />CO6: Able to apply the Laplace transform and Z-transform for analyzing of continuous-time and discrete-time signals and systems.
Essential Reading
- A. V. Oppenheim, A. S. Willsky and S. H. Nawab, Signals and Systems, Pearson , Second Edition, 2015.
- Simon Haykin and B. V. Veen, Signals and Systems, Wiley , Second Edition, 2007.
Supplementary Reading
- M. J. Roberts, Fundamentals of Signals and Systems, McGraw Hill , 2007
- B.P. Lathi, Principles of Linear Systems and Signals, Oxford , Second edition, 2009