The following model is commonly assumed in communica- tion systems. Consider a system with input x(t)...

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The following model is commonly assumed in communica- tion systems. Consider a system with input x(t) and output y(t) defined by the equation where T> 0. 1 y(t) = Σ ( 1² ) |k| x(t – kT) a. Prove that the system is linear b. Prove that the system is time-invariant c. Find the impulse response h(t). Plot h(t). d. Is the system causal? Why or why not? e. Is the system BIBO stable? Why or why not? f. Suppose x(t) = u(t) in which u(t) is the unit-step signal. Find the corresponding y(t) for this particular input. g. Sketch y(t). The following model is commonly assumed in communica- tion systems. Consider a system with input x(t) and output y(t) defined by the equation where T> 0. 1 y(t) = Σ ( 1² ) |k| x(t – kT) a. Prove that the system is linear b. Prove that the system is time-invariant c. Find the impulse response h(t). Plot h(t). d. Is the system causal? Why or why not? e. Is the system BIBO stable? Why or why not? f. Suppose x(t) = u(t) in which u(t) is the unit-step signal. Find the corresponding y(t) for this particular input. g. Sketch y(t).

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