Q2 (a) Given two signals; x₁(t)=eatu(t), a > 0 and x2(t)=ebu(t),b> 0 where a b. If x(t) is an output of a convolution process between x₁ (t) and x2(t), that is x(t) = x(t) + x2(t). Find: (i) Fourier transform of x(t). (ii) Signal x(t) using inverse Fourier transform of signal in Q2(a)(i). (b) A basic modulator circuit is shown in Figure Q2.1. Modulation is a multiplication between voltage signal, v(t), and a carrier signal, c(t). The process yields an output signal, m(t). v(t) = sinc(t) c(t) = cos(wet) m(t) (i) Figure Q2.1. Analyze the Fourier transform of output signal, m(t) by using modulation properties. (ii) Sketch the spectrum signal of M(w). (c) Analyze the output voltage, v,(t) of the electrical circuit shown in Figure Q2.2 for the input voltage vi(t) 3e stu(t) V w 3Ω DC . V₁(t) 2F V(t) Figure Q2.2 3