2. The continuous-time signal x(t) = cos(2000πt) is sampled with sampling period T to obtain a discrete-time signal r[n] = cos("/3). a) Determine a choice of T, consistent with this information. Justify your answer. b) For your choice of T, in (a), sketch the spectrum of the sampled signal x[n] (i.e., show the alias frequencies) as a function of normalized frequency for -2π <<2. Carefully and completely label your plot. c) Is your choice for T, in part (a) unique? If not, specify another choice of T consistent with the information given. 3. Consider a discrete-time system with input-output relationship y[n] = 2x[n] - 3x[n-1]+2x[n-2] where the input signal is a[n] and the output signal is y[n]. Please review the homework format rules in the syllabus to ensure that your work conforms to them. 1 a) Draw two block diagrams that represent this system in terms of unit-delay elements, coefficient multipliers and adders. Draw one diagram in direct form, and the other in transposed-direct form.

Fig: 1