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# Principles of Signals and Systems

### Overview

This course is introduces the fundamental principles of signals and system analysis. These concepts form the building blocks of modern digital signal processing, communication and control systems. Hence, a sound understanding of these principles is necessary for all students of Electronics and Communication engineering (ECE), Electrical and Electronics Engineering (EEE), and Instrumentation Engineering (IE). The course will cover various basic tools of signal and system analysis such as signal classification, LTI systems, Properties of LTI Systems, Frequency Response, Laplace Transform, Z-Transform, Fourier Transform, Fourier Series, Discrete Time Fourier Transform (DTFT), Discrete Fourier Transform (DFT), Cascade/ Parallel structures and their various practical applications. Various concepts such as convolution, impulse/ frequency response, causality, stability of systems will be especially emphasized. Other additional topics such as state space techniques and solutions to state space equations will also be covered.This course is suitable for all UG/PG students and practicing engineers/ managers who are looking to build a solid grasp of the fundamental concepts of signals and systems as well as students/ professionals preparing for their college/ university/ competitive exams.INTENDED AUDIENCE :Students in Electrical Engineering, Electronics and Communication EngineeringPracticing engineersTechnical and Non-technical managers of telecomm companiesStudents preparing for competitive exams with Signals and Systems subjectPREREQUISITES : Basic knowledge of Integration, Differentiation, Complex NumbersINDUSTRY SUPPORT : Most companies in Electronics, Communication and Signal Processing. Examples are Qualcomm, Broadcom, Intel, Sasken etc.

### Syllabus

Week 1:Introduction to Signals, Signal Classification, Continuous/ Discrete Time Signals
Week 2:Definition and Classification of Systems, Linear Time Invariant (LTI) Systems
Week 3:Properties of LTI Systems, Impulse Response, Convolution, Causality, Stability
Week 4:Impulse Response of Discrete Time Systems, Discrete Time Convolution, Difference Equations and Analysis
Week 5: Laplace Transform, Properties of Laplace Transform, Inverse Laplace Transform
Week 6:Introduction to z-Transform, Properties of z-Transform, Region of Convergence, Inverse z-Transform
Week 7:Introduction to Fourier Analysis, Fourier Series for Periodic Signals, Properties of Fourier Series
Week 8: Introduction to Fourier Transform, Properties of Fourier Transform, Frequency Response of Continuous Time Systems, Examples of Frequency Response
Week 9: Fourier Analysis of Discrete Signals, Discrete Time Fourier Transform (DTFT), Properties of DTFT, Examples of DTFT
Week 10: Frequency Response of Discrete Time Systems, Discrete Fourier Transform (DFT), Properties of DFT, Examples of DFT
Week 11:IIR/ FIR Filters, Direct Form Realization, Cascade and Parallel Form Realization, Problem Solving
Week 12:Concept of State, State Space Analysis, State Space Representation of Continuous Time Systems, Solution of State Equations for Continuous Systems