Need MATLAB code of the following 4.17 Consider the following discrete-time signal. I = (1,2, 1,0 (a)

Need MATLAB code of the following 

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4.17 Consider the following discrete-time signal. I = (1,2, 1,0" (a) Find X(i) = DFT{r(k}}. (b) Compute the magnitude spectrum A,(i). (c) Compute the phase spectrum 6,(i). (d) Compute the power density spectrum S,(i). Solution (a) Here W4 exp(-j27/4) = -j. Using Definition 4.2 X (0) = 1+2+1 = 4 3. (b) The magnitude spectrum of r(k) is X(1) = 1+2(-j)+ 1(-1) = -j2 A = |X| [4, 2, 0, 2" 3 X(2) = 1+2(-1) + 1(1) (c) The phase spectrum of z(k) is = 0 3 X(3) = Er(k)(W)* A = LX (0, -7/2,0, 7/2)" = 1+2(j)+1(-1) %3D = j2 (d) The power density spectrum of r(k) is Thus the DFT of r(k) is |XP/4 (4, 1,0, 1]" SN = X = [4, -j2,0, j2j" %3D 4.17 Consider the following discrete-time signal. I = (1,2, 1,0" (a) Find X(i) = DFT{r(k}}. (b) Compute the magnitude spectrum A,(i). (c) Compute the phase spectrum 6,(i). (d) Compute the power density spectrum S,(i). Solution (a) Here W4 exp(-j27/4) = -j. Using Definition 4.2 X (0) = 1+2+1 = 4 3. (b) The magnitude spectrum of r(k) is X(1) = 1+2(-j)+ 1(-1) = -j2 A = |X| [4, 2, 0, 2" 3 X(2) = 1+2(-1) + 1(1) (c) The phase spectrum of z(k) is = 0 3 X(3) = Er(k)(W)* A = LX (0, -7/2,0, 7/2)" = 1+2(j)+1(-1) %3D = j2 (d) The power density spectrum of r(k) is Thus the DFT of r(k) is |XP/4 (4, 1,0, 1]" SN = X = [4, -j2,0, j2j" %3D

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