1. Signals and Systems Using MATLAB Luis F. Chaparro

2. Chapter 4 - Frequency Analysis The Fourier Series

3. What is in this chapter? Eigenfunctions and LTI systems
Complex and trigonometric Fourier Series
Line spectrum: distribution of power over frequency
Laplace and Fourier Series
Properties of Fourier Series
Response of LTI systems to periodic signals 3

4. Eigenfunctions revisited4

5. 5

6. 6

7. 7

8. 8

9. 9

10. 10

11. 11

12. 12

13. 13

14. 14

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17. 17

18. 18

19. 19

20. 20

21. Application in communications21

22. 22

23. input sinusoid
ss output sinusoid
of same frequency 23

24. 24

25. magnitude and phase at
harmonic frequency
input
output 25

26. 26

27. 27

28. 28

29. 29

30. What have we accomplished?
Sinusoidal representation of periodic signals
Eigenfunction property of LTI systems
Response of LTI systems to periodic signals
Connection of Fourier series and Laplace transform
Inverse time frequency relation
Where do we go from here?
Extension of Fourier representation for aperiodic signals
Unification of spectral theory for periodic and aperiodic signals
Convolution and frequency response of LTI systems
Connection of Laplace and Fourier transforms 30