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Question 1: 1.1 The input to a digital system is x[n] = a(2)" u[n], find the average energy of the signal. (3) 270 2.2 Consider the following signal y[n] = $cos =ß cos 4 find the average power of the signal. 4 (3) 2.3 Show analytically using appropriate formulae the odd and even components of the following signal. x[n] = anj sin(n) [cos(na) (4) 2.4 Analyse the following signal x(t)= a cos(57).ß sin(107), find the critical sampling rate (4) 2.5 A 120Hz sinusoid signal is sampled at 65 Hz, show mathematically that aliasing has occurred. Indicate if the signal is in phase or out of phase. Consider that the sinusoid is x(t) = sin(27 +) (4) 2.6 If y[n] = sin(0.3751 Vin), determine if the signal is periodic. State reasons (2) [20]