Question

Problem 3 Consider the following system. OCE] 2 ) you] aa a - Assume that the input is the sinusoidal sequence and shown above. Plot the output y[n] for n = -6, -5,..., 6 by specifying its exact amplitude values. b - Find a (nonzero) sinusoidal input x[n] that is canceled by this system. Plot it for n = -6, -5,..., 6 by specifying its exact amplitude values.

Answer 1

from the block diagram. & and each other X12) E(2) Ecz) = Y(z) +67+2) E(2) 8 X(2)__ = [17).. Y(z) = E(2) + ' E(2) + 2EC2) You = (1+z²+z²) E(2) . H(2)= You : Hatice w and at 2 Sin (2009). N=6. mm] 2 sin cng) = 73 Yinde | Hausloa sin(n + _ Hershefcio). Thas coping s ite jaus i + [e3093es 2015 7-e 53 Et 1 Hiz)] = 3 11 1992 = 6 LM2l = tant (-43) = -1 So yłn} = HB sin (97-73) = 452 sn (14)

So plot of yn) = 6 a (n-1) totajpillot -4 -3 -2 L P 1 2 3 4 5 b. to canced the input a outpat Sin(n-1) =0 =) (n-1)/3 = 27k k=0,1,2,3... ht=6k Th=6kH so x[n] = sin (160H) a) is canceled. a(n) = sin (ann + Tre)
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