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Fourier Series: Examples
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Factor: 1/ (1/2)Sin 2 Sin =
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Sin + (1/2)Sin 2
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Sin + (1/2)Sin 2 + (1/3)Sin 3 + (1/4)Sin 4
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6 terms of the series
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10 terms of the series
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20 terms of the series
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Factor: 4/ Sin (1/3)Sin3
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Sin + (1/3)Sin3
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Sin +(1/3)Sin3 +(1/5)Sin5 +(1/7)Sin7
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6 terms of the series
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10 terms of the series
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20 terms of the series
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Cos + (1/9)Cos 3 Factor: 8/ 2
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Cos + (1/9)Cos 3 + (1/25)Cos 5 + (1/49)Cos 7
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8 terms of the series
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Fourier Series: f(t), t < < T f(t) =A0 + A1 Cos A2 Cos 2 + A3 Cos A4 Cos ……. + B1 Sin B2 Sin B3 Sin … f(t) A0 = f(t) Cos n An / 2 =
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Orthogonality relations
Bm / 2 = f(t) Sin m Cos n Sin m = 0 Cos n Cos m = 0 Sin n Sin m = 0 n and m are different Orthogonality relations
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