Consider a discrete-time system with output y[n] given by y[n] = x[n] f[n] and x[n] is the
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Consider a discrete-time system with output y[n] given by y[n] = x[n] f[n] and x[n] is the input and f[n] is a function.
(a) Let the input be x[n] = 4cos (πn/2) and f[n] = cos (6πn/7), −∞ < n < ∞. Is x[n] periodic? If so, indicate its fundamental period N0. Is the output of the system y[n] periodic? If so, indicate its fundamental period N1.
(b) Suppose now that f[n] = u[n] − u[n − 2] and x[n] = u[n]. Determine if the system with the above input-output equation is time-invariant.
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a xn is periodic of fundamental period N 0 4 and f n is peri...View the full answer
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