Signals and Systems M. Rahmati Computer Engineering and Information Technology Department Amir Kabir...

Signals and Systems

M. RahmatiComputer Engineering and Information Technology DepartmentAmir Kabir University of Technology(Tehran Polytechnic)

rahmati@aut.ac.ir

Spring 1391

Course organization

Textbook◦ Signals and Systems

Alan V. Oppenheim Alan S. Willsky S. Hamid Nawab

References◦ Fundamentals of Signals and Systems: Using Matlab

Edward W. Kamen and bonnie S. Heck Prentice Hall

◦ Signals and Systems : Continuous and Discrete Ziemer, Trainer, Fannin Macmillon

Course organization Grading

◦ Homework (20%) Computer Projects

Matlab, Java, C, C++ DO NOT COPY other students’ codes Add Comments to all of your source codes

Written Problems

◦ Tests (70 %) First Exam Midterm (Closed book) Final (Closed Book)

◦ Computer Project

Course organizationPolicies

◦Attendance◦Late Attendance◦Missing Exams / HW◦Neatness◦INDIVIDUALLY of your works◦NO CELL PHONE

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Overall Outline Introduction 1. Signals 2. Systems 3. Continuous-time Fourier Transform 4. Communication Systems 5. Discrete-Time Fourier Transform 6. Sampling 7. Applications of Discrete-Time Signal Processing 8. Fourier Series Representation 9. Laplace Transform 10. Feedback Systems 11. Z-Transform

What is“Signals & Systems”all about???

SIGNALS

Signals are functions of independent variables that carry information. For example:

Electrical signals ---voltages and currents in a circuit

Acoustic signals ---audio or speech signals (analog or digital)

Video signals ---intensity variations in an image (e.g. a CAT scan)

Biological signals ---sequence of bases in a gene

..

Beyond “Signals & Systems”

Signals & systems

Control system

Communication system

Digital Signal

Processing

Analog Electroni

csFPGAs for DSP

Computer Networks

Computer Security

Computer Paradigms

(AI, Neural Net., Etc.

Some Application Areas

Five Common Signals & Systems Scenarios:

Signal Classification :Type of Independent Variable

Time is often the independent variable. Example: the electrical activity of the heart recorded with chest electrodes –– the electrocardiogram (ECG or EKG).

The variables can also be spatial

Independent Variable Dimensionality

Continuous-Time & Discrete-Time

Our Studies

THE INDEPENDENT VARIABLES

CT Signals

DT Signals

Our Notation :

Many human-made DT Signals

Why DT? —Can be processed by modern digital computers and digital signal processors (DSPs).

Mandrill Example

Mandrill Example

Image Processing in Digital Camera

SYSTEMS For the most part, our view of systems

will be from an input-output perspective:

A system responds to applied input signals, and its response is described in terms of one or more output signals

EXAMPLES OF SYSTEMS

SYSTEM INTERCONNECTIOINS

Real and Complex Signals