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20-5553: Fourier Analysis – page 6

20-5553: Fourier Analysis – page 6. Period=2L :. Period=2  :. 20-5553: Dynamical Systems and Fourier Analysis. Deriving the formula for a n :. Start with the Fourier series formula:. , where n is an integer. Multiply each term by cos( mt ), where m is also an integer.

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20-5553: Fourier Analysis – page 6

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  1. 20-5553: Fourier Analysis – page 6 Period=2L : Period=2 : 20-5553: Dynamical Systems and Fourier Analysis

  2. Deriving the formula for an: Start with the Fourier series formula: , where n is an integer Multiply each term by cos(mt), wheremis also an integer Now integrate from - to : 20-5553: Dynamical Systems and Fourier Analysis

  3. Now, we also know that and also that so therefore: and hence: 20-5553: Dynamical Systems and Fourier Analysis

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