## COURSE OBJECTIVES

The objective of this course is to develop the understanding of the basic ideas of the Signals & Systems encountered in engineering. The main focus will be on the methods for characterizing and analyzing continuous-time and discrete time signals and systems. Students will learn some transform techniques (Laplace transform, Z-transform and Fourier transform) that are useful for the understanding of Digital communication systems, Feedback control systems, Satellite and mobile communications, Digital signal processing and Digital image processing.

### COURSE LEARNING OUTCOMES (CLO)

CLO 1: Express the concepts of signals and systems and their different types which can be used in a wide variety of disciplines in engineering. (Level: C2)

CLO 2: Identify and report system properties such as causality, stability, linearity, and time invariance etc. (Level: C3)

CLO 3: Apply the convolution sum/convolution integral formulas to determine the output of continuous time/discrete time systems. (Level: C4)

CLO 4: Analyze continuous and discrete time signals and systems in the time/frequency-domain using Fourier, Laplace and z-transforms.

## COURSE CONTENTS

1. Fundamental Concepts of Signals & Systems-Six Lectures
• Introduction
• Signals and Their Classification
• Basic Continuous and Discrete Time Signals
• Operations on Signals
• Systems and Classification of Systems
• Interconnections of Systems
2. Linear Time Invariant Systems- Eight Lectures
• Response of a Continuous Time LTI System and Convolution Integral
• Properties of Continuous and Discrete Time LTI System
• Response of a Discrete Time LTI System and Convolution Sum
• Eigen function of Continuous and Discrete Time LTI System
• Properties of Convolution
• Systems Described by Difference and Differential Equations
3. Laplace Transform and Continuous Time LTI Systems-Four Lectures
• The Laplace Transform
• Laplace Transform of Some Common Signals
• Properties of Laplace Transform
• The Inverse Laplace Transform
• The System Function
• The Unilateral The Laplace Transform
• Solving Differential Equations by Using Laplace Transform
4. The z-Transform and Discrete Time LTI Systems- Four Lectures
• The z-Transform
• z-Transform of some Common Signals
• Properties of z-Transform
• The Inverse z-Transform
• The System Function of Discrete Time LTI System
• The Unilateral z-Transform
• Solving Difference Equations by Using z-Transform
5. Fourier Analysis of Continuous Time Signals and Systems- Four Lectures
• Fourier Series Representations of Periodic Signals
• The Fourier Transform
• Properties of Continuous time Fourier Transform
• The Frequency Response of Continuous Time LTI Systems
• Filtering and Bandwidth
• Modulation
• Sampling Theorem
6. Fourier Analysis of Discrete Time Signals and Systems- Six Lectures
• Discrete Fourier Series
• Discrete Time Fourier Transform (DTFT)
• Properties of Discrete Time Fourier Transform
• The Frequency Response of Discrete time LTI Systems
• Discrete Fourier Transform (DFT)
• Properties of Discrete Fourier Transform (DFT)
• Circular Convolution
• Fast Fourier Transform (FFT)