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Consider a system with the input/output relationship y(t) = x(t)cos(15?t). (a) Is this system (i) linear, (ii)...

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Advance Math

Consider a system with the input/output relationship y(t) =x(t)cos(15?t).
(a) Is this system (i) linear, (ii) causal, (iii) stable, (iv)memoryless, (v) time-invariant, and (vi) invertible. Justify eachanswer with a clear mathematical argument. (b) Find the FourierTransform Y (f) of y(t) in terms of the transform X(f) of x(t).

Repeat problem (2) for the system with the input-outputrelationship y(t) =R1 ?=0(1??)2x(t??)d?.

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