FourierSeriesExample

FourierSeriesExample - We briefly demonstrate that a...

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Unformatted text preview: We briefly demonstrate that a function can be approximated by a summation of sine and cosine functions with varying frequency and amplitude. 1.2 x(t) x0 + x (t)+ x (t) + x (t) 1 2 3 1 0.8 0.6 0.4 0.2 0 -0.2 -10 -8 -6 -4 -2 0 time 2 4 6 8 10 1 x0 0 -1 1 x1(t) 0 -8 -6 -4 -2 0 2 4 6 8 -1 1 x2(t) -8 -6 -4 -2 0 2 4 6 8 0 -1 1 x3(t) 0 -8 -6 -4 -2 0 2 4 6 8 -1 -8 -6 -4 -2 0 time 2 4 6 8 Consider the periodic function that is defined for The function has period exponential Fourier series where We compute the Fourier coefficients, and , and fundamental frequency . We wish to compute the Fourier series with coefficients 1 x(t) Fourier series 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -10 -8 -6 -4 -2 0 time 2 4 6 8 10 0.25 0.2 magnitude D(n) 0.15 0.1 0.05 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 3 2 angle D(n) 1 0 -1 -2 -3 -1 -0.8 -0.6 -0.4 -0.2 0 n 0.2 0.4 0.6 0.8 1 Fourier series with coefficients 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -10 x(t) Fourier series -8 -6 -4 -2 0 time 2 4 6 8 10 0.25 magnitude D(n) 0.2 0.15 0.1 0.05 0 -3 -2 -1 0 1 2 3 4 2 0 -2 -4 -3 angle D(n) -2 -1 0 n 1 2 3 Fourier series with coefficients 1.2 x(t) Fourier series 1 0.8 0.6 0.4 0.2 0 -0.2 -10 -8 -6 -4 -2 0 time 2 4 6 8 10 0.25 0.2 magnitude D(n) 0.15 0.1 0.05 0 -8 -6 -4 -2 0 2 4 6 8 4 3 2 angle D(n) 1 0 -1 -2 -3 -8 -6 -4 -2 0 n 2 4 6 8 Fourier series with coefficients 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -10 x(t) Fourier series -8 -6 -4 -2 0 time 2 4 6 8 10 0.4 magnitude D(n) 0.2 0 -100 5 -80 -60 -40 -20 0 20 40 60 80 100 angle D(n) 0 -5 -100 -80 -60 -40 -20 0 n 20 40 60 80 100 ...
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