O&WwN Problem 1.22. parts (a), (b), (e) and (f) only. Also, sketch the following signals using Figure P1.22: epsilon v {x[n]}, 2 – x[n], 3x[n]. Indicate for each of the following signals whether it is periodic. If so, give the period N. x_1[n] = sin((3 pi/4)n) x_2[n] = e^j(7 pi/5)n x_3[n] = e^j(2 pi/7)n u[n] x_4[n] = cos(2n) x_5[n] = cos((3 pi/7)n) + sin ((4 pi/5)n). For each of the systems listed below, determine which of the following properties hold: (1) Time-invariance, (2) Linearity, (3) Causality, and (4) Stability. If you say that a property holds for a system, justify your answer with a clear proof. If you say that a property does not hold, justify your answer either with a proof or a counter-example. y[n] = x[-n] y[n] = x[n -2] – 2x[n – 8] y[n] = nx[n] y[n] = x[n] delta [n – 3]

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