1. Signals and Systems M. Rahmati Computer Engineering and Information Technology Department Amir Kabir University of Technology (Tehran Polytechnic) rahmati@aut.ac.ir Spring 1391

2. 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

3. 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

4. Course organization Policies ◦ Attendance ◦ Late Attendance ◦ Missing Exams / HW ◦ Neatness ◦ INDIVIDUALLY of your works ◦ NO CELL PHONE  Turn your mobile OFF

5. 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

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

7. 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.

8. Beyond “Signals & Systems” Signals & systems Control system Communication system Digital Signal Processing Analog Electronics FPGAs for DSP Computer Networks Computer Security Computer Paradigms (AI, Neural Net., Etc. Computer Paradigms (AI, Neural Net., Etc.

9. Some Application Areas

10. Five Common Signals & Systems Scenarios:

11. 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).

12. The variables can also be spatial

13. Independent Variable Dimensionality

14. Continuous-Time & Discrete- Time

15. Our Studies

16. THE INDEPENDENT VARIABLES

17. CT Signals

18. DT Signals Our Notation :

19. Many human-made DT Signals Why DT? —Can be processed by modern digital computers and digital signal processors (DSPs).

20. Mandrill Example

22. Image Processing in Digital Camera

23. 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

24. EXAMPLES OF SYSTEMS

25. SYSTEM INTERCONNECTIOINS

26. Real and Complex Signals