1 (a) (b) x₁ (t) Consider the system shown in Figure Q1(a)(i), where the frequency response H(w) has magnitude as shown

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1 A B X T Consider The System Shown In Figure Q1 A I Where The Frequency Response H W Has Magnitude As Shown 1 (83.7 KiB) Viewed 25 times

1 (a) (b) x₁ (t) Consider the system shown in Figure Q1(a)(i), where the frequency response H(w) has magnitude as shown in Figure Q1(a)(ii). Given x₁ (t) = cos (nt) and x₂ (t) = cos (2nt). (1) (ii) (iii) x₂ (1) 2 Figure Q1(a)(i) Determine the mathematical expression of x(t) and its corresponding Fourier transform X(w). (4 marks) Sketch the magnitude spectrum of Y(w). Determine the output signal, y(t). By using the Fourier transform, calculate the voltage, v(t) and the current, i(t) in the circuit shown in Figure Q1(b) when the input, e(t) = u(t)-u(t-2) V. -4x Figure Q1(a)(ii) H(o) 1- M 4 x(t) H(@) y(t) (6 marks) @(rad/s) (3 marks) (7 marks)