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Continuous-time Fourier Series

Continuous-time Fourier Series. Prof. Siripong Potisuk. Orthogonal Expansion of CT Signals. A linear combination of weighted orthogonal basis functions. Orthogonal Basis Functions. Periodic Complex Exponentials. Continuous-time Fourier Series.

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Continuous-time Fourier Series

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  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

  6. 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?

  7. Minimum Mean Square Error (MMSE)

  8. Fourier series coefficients

  9. Dirichlet Conditions

  10. Gibbs phenomenon

  11. Example1 • Find the complex Fourier series coefficients of the signal

  12. Example 2 • Find the complex Fourier series coefficients of the signal

  13. Example 3 • Find the complex Fourier series coefficients of the signal

  14. Example 3: Line Spectrum

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