QUESTION 1 Q 1(a) Obtain the z-Transforms of each of the following signals ITOTAL MARKS: 25] [6 Marks In] = cos (-_-) uln] 2 marks] u nun – marks] 0-S Q 1(b) The signal x[n], (of length 4 samples) is defined as: x[n-(1,-1,12) [7 Marks] (i) Write down the Discrete-time Fourier Transform (DTFT) of xn [2 marks] (i) pn] is the periodic sequence (of period 4 samples) obtained by 5 marks] repeating xIn]. What is the DTFT of [n]? Q 1(c) [8 Marks] 1/2 Figure Q1 Determine [4 marks] [2 marks] 2 marks] (0) the transfer function, (ii) the pole-zero diagram (ii) the difference equation of the system shown in Figure Q1 Q 1(d) [4 Marks] Let X(z) be the z-Transform of the sequence x[n] = u[n] (0.5)”. Using the table of z-Transforms and properties, find the sequences f[n] and g[n whose z-Transforms are F(z) z-3x(z), and G(z) – X(-3z) respectively [End of Question 1]