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 [70 pts] For the following systems please determine if the system is: (1) stable, (2) Causual, (3) linear, (4) time invariant, and (5) memoryless. Please explain why.
(a) Tx[n] = Σn k=n0x[k] where n 6= 0. (b) Tx[n] = Σn+n0 k=n−n0 x[k]. (c) Tx[n] = x[n−n0]. (d) Tx[n] = ex[n]. (e) Tx[n] = ax[n] + b. (f) Tx[n] = x[−n]. (g) Tx[n] = x[n] + 3u[n−1]. Problem 2: [20 pts] Given the difference equatoin: y[n]− 3 4y[n−1] + 1 8y[n−2] = 2x[n−1] . Determiney [n] for n ≥ 0 when x[n] = δ[n] and y[n] = 0 for n < 0. Problem 3: [40 pts] Show weither the following signals are periodic. If the signal is periodic, what is the period?
(a) x[n] = ej(πn/6) (b) x[n] = sin(πn/5) πn (c) x[n] = ej(3πn/4) (d) x[n] = ejπn/√2

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