Chapter 1: Introduction to Digital Signal Processing 1. A Discrete-time signal x[n]=[0,1,2,3,2,1,0,0,0] is shown in Figure 1 below, sketch and label each of the signal in (a)-(d). a) x[n2] b) x[2n] c) x[n+2] d) x[0.5n3] 2. Determine if the following discrete-time signals are periodic or aperiodic. If is periodic, find the sample period N of the signals. a) x[n]=ein/6 b) x[n]=cos(n2+6) c) x[n]=sin(73n8) d) x[n]=cos(n2+6)+e6in 3. a) Decompose the discrete-time signal x[n] given by a sequence x[n]= [2,8,2,4,5,2,7] into its odd and even components. b) Prove that the sum of the decomposed signals in 3(a) is equals to the original sequence x[n]