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EED1004- Introduction to Signals Instructor: Dr. Gülden Köktürk Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING.

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Presentation on theme: "EED1004- Introduction to Signals Instructor: Dr. Gülden Köktürk Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING."— Presentation transcript:

1 EED1004- Introduction to Signals Instructor: Dr. Gülden Köktürk Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING

2 COMPLEX NUMBERS Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING

3 Rectangular Notation for Complex Numbers Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING

4 Polar Notation for Complex Numbers Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING

5 Conversion between Rectangular and Polar Notations

6 Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING Examples

7 Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING

8 EULER’S FORMULA

9 Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING Examples

10 Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING Conversion between Degrees and Radians

11 Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING Inverse Euler Formulas

12 Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING ALGEBRAIC RULES FOR COMPLEX NUMBERS

13 Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING

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16 GEOMETRIC VIEWS OF COMPLEX OPERATIONS Addition: (4-j3)+(2+j5)=6+j2 What is the addition of following four complex numbers? (1+j)+(-1+j)+(-1-j)+(1-j)=?

17 Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING

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21 POWERS AND ROOTS

22 Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING De Moivre’s Formula

23 Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED1004-INTRODUCTION TO SIGNAL PROCESSING

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