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.]

To understand the fundamental characteristics of signals and systems.

To understand signals and systems in terms of both the time and transform domains.

To develop the mathematical skills to solve problems involving convolution, filtering, and sampling.

CO1: Able to understand the fundamental characteristics of continuous-time and discrete-time signals and systems.
CO2: Able to classify systems based on their properties and determine the response of LTI system using convolution.
CO3: Able to analyze the spectral characteristics of continuous-time periodic and aperiodic signals using Fourier analysis.
CO4: Able to understand the process of sampling and the effects of under sampling.
CO5: Able to apply the Laplace transform and Z-transform for analyzing of continuous-time and discrete-time signals and systems.

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.

M. J. Roberts, Fundamentals of Signals and Systems, McGraw Hill , 2007

B.P. Lathi, Principles of Linear Systems and Signals, Oxford , Second edition, 2009