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 (n/2) and f[n] = cos (6n/7), < n < . Is x[n] periodic? If so, indicate its fundamental period N 0 . Is the output of the system y[n] periodic? If so, indicate its fundamental period N 1 . (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.

Question: 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

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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