1. A rectangular pulse train g(t) shown in Figure 1 has amplitude A = 1V, period...

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1. A rectangular pulse train g(t) shown in Figure 1 has amplitude A = 1V, period T₁ = 1 ms, and pulse width t = 0.62 ms. The rectangular pulse train has a delay of t = 0.31 ms. The signal g(t) is applied to a circuit shown in Figure 2. The output of the circuit is y(t). Let R = 360 W, L = 8 mH. (a) Find the numerical values of gc, gq, of g(t) for 0≤n≤ 5. (b) Represent g(t) as a sum of dc component, fundamental component, 2nd harmonic component, and 3 harmonic component. The coefficients must be numbers. (c) Find the transfer function H(w) of the circuit shown in Figure 2. (d) Find the numerical values of H(nw) and ĐH(nw) for 0 <n ≤5. w. = 2p/T. (e) Find the magnitude yc and phase yq, of the trigonometric Fourier coefficients of the output y(t) for 0 ≤ n ≤ 5. (f) Represent y(t) as a sum of de component, fundamental component, 2nd harmonic component, and 3rd harmonic component. The coefficients must be numbers. 1 0.5 0 -2 Figure 1 Figure 2 -1.5 -1 -0.5 0 t 0.5 1 1.5 2 X x 103 1. A rectangular pulse train g(t) shown in Figure 1 has amplitude A = 1V, period T₁ = 1 ms, and pulse width t = 0.62 ms. The rectangular pulse train has a delay of t = 0.31 ms. The signal g(t) is applied to a circuit shown in Figure 2. The output of the circuit is y(t). Let R = 360 W, L = 8 mH. (a) Find the numerical values of gc, gq, of g(t) for 0≤n≤ 5. (b) Represent g(t) as a sum of dc component, fundamental component, 2nd harmonic component, and 3 harmonic component. The coefficients must be numbers. (c) Find the transfer function H(w) of the circuit shown in Figure 2. (d) Find the numerical values of H(nw) and ĐH(nw) for 0 <n ≤5. w. = 2p/T. (e) Find the magnitude yc and phase yq, of the trigonometric Fourier coefficients of the output y(t) for 0 ≤ n ≤ 5. (f) Represent y(t) as a sum of de component, fundamental component, 2nd harmonic component, and 3rd harmonic component. The coefficients must be numbers. 1 0.5 0 -2 Figure 1 Figure 2 -1.5 -1 -0.5 0 t 0.5 1 1.5 2 X x 103