1. Continuous-time Fourier Series Prof. Siripong Potisuk

2. Orthogonal Expansion of CT Signals A linear combination of weighted orthogonal basis functions

3. Orthogonal Basis Functions

4. Periodic Complex Exponentials

5. Continuous-time Fourier Series A linear combination of harmonically related complex exponentials is an approximation or estimate to the given periodic signal

8. Continuous-time Fourier Series How good is in approximating ? Is it possible to obtain an exact representation of in the form of ?  # of basis functions (harmonics) needed  convergence of Fourier Series with an infinite # of harmonics How does one obtain the coefficients?

9. Minimum Mean Square Error (MMSE)

10. Fourier series coefficients

11. Dirichlet Conditions

13. Gibbs phenomenon

14. Example1 Find the complex Fourier series coefficients of the signal

15. Example 2 Find the complex Fourier series coefficients of the signal

16. Example 3 Find the complex Fourier series coefficients of the signal

17. Example 3: Line Spectrum