A signal g(t) is produced by switching on a continuous-time signal v(t) for a limited time -0.5T ≤ t ≤ 0.5T. 1) How can one produce g(t) from v(t) in the time domain? 2) Let G(j) and V(j) are the Fourier transforms of g(t) and v(t). Derive an expression for G(j) in terms of V(j).

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You are an electrical engineer now and are receiving a communication signal. You find that the signal can be formulated as f(x) =[8(x-2)+8(x+2)] (1) Your team leader asks you to analyze the result of the particle movement in the frequency domain. You first decide to apply the Fourier Transform to do this job. Please show your result after applying the Fourier Transform. (2) While receiving the signal, you adopt a circuit to process this signal. After your analysis, you can model the circuit by using the following ordinary differential equation (ODE). Please solve it. y'(x)+3y'(x)+2y(x) =[8(x-2)+8(x+2)] 2i

This is a practice question from the Signal and Systems course of my Electrical Engineering Program. Could you please walk me through the steps for solving this? Thank you for your assistance.