(a) Consider a system with input x(t) and with output y(t) given by +00 y(t) =...

 

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(a) Consider a system with input x(t) and with output y(t) given by +00 y(t) = x(t)(tn) 12=-0 (i) Is this system linear? (ii) Is this system time-invariant? For each part, if your answer is yes, show why this is so. If your answer is no, produce a counterexample. 1 1 1 1 (b) Suppose that the input to this system is x(t) = cos 2πt. Sketch and label carefully the output y(t) for each of the following values of T: T = 1,412 All of your sketches should have the same horizontal and vertical scales. (c) Repeat part (b) for x(t) = e' cos 2πt. (a) Consider a system with input x(t) and with output y(t) given by +00 y(t) = x(t)(tn) 12=-0 (i) Is this system linear? (ii) Is this system time-invariant? For each part, if your answer is yes, show why this is so. If your answer is no, produce a counterexample. 1 1 1 1 (b) Suppose that the input to this system is x(t) = cos 2πt. Sketch and label carefully the output y(t) for each of the following values of T: T = 1,412 All of your sketches should have the same horizontal and vertical scales. (c) Repeat part (b) for x(t) = e' cos 2πt.