1. Fourier Series 4.2-4.3

2. Motivation (Time Domain Representation) (Frequency Domain Representation)

3. Goal

4. Connection to Calc (Taylor Series)

5. Introductory Example

6. Details

7. Fourier Coefficients

8. Methods of Calculating the Fourier Series Coefficients

9. Fourier Series of Impulse Train

11. Fourier Series of a Square Wave Co is a DC average.

12. Details (1)

13. Details (2)

14. Details (3)

15. Gibbs Phenomenon

16. Gibbs Phenomenon (2)

17. Fourier Series Coefficient K=-5, Ck=2jV/(5π) K=-3, Ck=2jV/(3π) K=-1, Ck=2jV/π K=1, Ck=-2jV/π K=3, Ck=-2jV/(3π) K=5, Ck=-2jV/(5π)

18. Frequency Spectra K=-5, Ck=2jV/(5π) K=-3, Ck=2jV/(3π) K=-1, Ck=2jV/π K=1, Ck=-2jV/π K=3, Ck=-2jV/(3π) K=5, Ck=-2jV/(5π)

19. Use Matlab to Calculate Fourier Series Coefficient Integration from 0.5 to 1

20. Different Representations of Fourier Series

21. Rectangular Pulse

22. Sinc Function

23. Spectrum for a Rectangular Pulse Train

24. Peak Values of Sinc x