FourierSeriesExample

# FourierSeriesExample - 1.2 x(t x0 x(t x(t x(t 1 2 3 1 0.8...

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We briefly demonstrate that a function can be approximated by a summation of sine and cosine functions with varying frequency and amplitude. -10 -8 -6 -4 -2 0 2 4 6 8 10 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 time x(t) x 0 + x 1 (t)+ x 2 (t) + x 3 (t) -8 -6 -4 -2 0 2 4 6 8 -1 0 1 x 0 -8 -6 -4 -2 0 2 4 6 8 -1 0 1 x 1 (t) -8 -6 -4 -2 0 2 4 6 8 -1 0 1 x 2 (t) -8 -6 -4 -2 0 2 4 6 8 -1 0 1 time x 3 (t)

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Consider the periodic function that is defined for The function has period , and fundamental frequency . We wish to compute the exponential Fourier series where We compute the Fourier coefficients, and
Fourier series with coefficients -10 -8 -6 -4 -2 0 2 4 6 8 10 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 time x(t) Fourier series -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 0.05 0.1 0.15 0.2 0.25 magnitude D(n) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -3 -2 -1 0 1 2 3 angle D(n) n

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Fourier series with coefficients -10 -8 -6 -4 -2

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