**ELECTRICAL ENGINEERING**

Help needed in the following questions along with MATLAB plot

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Question 1 Check whether the following systems are linear or not: (a) y(n) = n x(n) (b) y(n) = x(n) +- 2x(n - 2) (c) y(n) = 2x(n) + 4 (d) y(n) = x(n) cos on N-1 (e) y(n) = Lx(n)l (f) y(n) = N x(n - k) *=0 Question 2 Determine whether the following discrete-time signals are periodic or not. If periodic, determine the fundamental period. (a) sin (0.02an) (b) sin (5an) (c) cos An (d) sin 2an 2n n -+ cos 3 5 (e) cos cos (f) cos +0.3n (g) el(2/2)n (h) I+ eizan3 _ jaxn/7 Question 3 Determine whether the following discrete-time signals are periodic or not. If periodic, determine the fundamental period. (a) sin (0.02an) (b) sin (5an) (c) cos An (d) sin -+ cos 2n n 3 (e) cos cos "it (f) cos ~ +0.3n (g) ela/2)n (h) 1+ e /2xw3 _j4an/7

Question 4 Find the convolution of the signals N n = - 2, 0, 1 x(n) = 3 n = -1 O elsewhere h(n) = 8(n) -28(n -1) + 38(n -2) - 8(n -3) Question 5 An interconnection of LTI systems is shown in Figure 2.14. The impulse responses are hi(n) = (1/2)" [u(n) - u(n - 4)]; h2(n) = 8(n) and hy(n) = u(n - 2). Let the impulse response of the overall system from x(n) to y(n) be denoted as h(n). (a) Express h(n) in terms of hi(n), h2(n) and hy(n). (b) Evaluate h(n). h,(n) x(n) y(n) h, (n) h,(n) Figure 2.14 System for Example 2.26. Question 6 Determine the convolution sum of two sequences: (1, 2, 2, 1] x(n) = (4, 2, 1,3), h(n) = T

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