Evaluate the Fourier coefficients n_p, a_s, and b_x for the periodic waveform sh

Question

Evaluate the Fourier coefficients n_p, a_s, and b_x for the periodic waveform shown in Figure 3 in the attached pdf file using the relation between the graph in Figure 3 and the corresponding graph in Figure 1. Now, verify your answers by evaluating the coefficients using MATLAB or 'direct' integration. Half-wave rectified sine wave: cog = 2x/T f(t) = A/k +A/2 sin cog f - 2A/x sigma^infinity_x = 1 cos(2 n cog I)/4 n^2 - 1 Full-wave rectified sine wave: w_g = 2x/T f(t) = 2A/x - 4A/k sigma^infinity_x = 1 cos(n cog I)/4n^2 - 1 Sawtooth wave: w_e = 2x/T f(t) = A/2 - A/k sigma^infinity_x = 1 sin (n w_g I)/n Triangle wave: w_g = 2x/T f(t) = A/2 - 4A/k^2 sigma^infinity_x = 1 cos ((2n - 1)w_g I/(2n - 1)^2

Explanation / Answer

By comparing the figure 1 to 1st function in trigonometric function list in above page,

It can be found that the waveform shown in figure 1 is delayed with t=2 and DC component added is 8. Note that, A=12 and T=20.

From above analysis and Fourier Series given above,

a0=(12/)+8=11.81818

a1=(12/2)=6

Others an coefficient are zero.

bn=(2 x 12/( x (1 - n^2))

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