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Find response of system using DTFT, h(n)=(12)nu(n);x(n)=(34)nu(n)
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Solution:

h(n)=(12)nu(n);x(n)=(34)nu(n)

H(ejω)=1112ejω;X(ejω)=1134ejωY(ejω)=H(ejω)X(ejω)

Y(ejω)=1112ejω1134ejω=ejωejω12ejωejω34Y(ejω)ejω=ejω(ejω12)(ejω34)=Aejω12+Bejω34ejω=A(ejω34)+B(ejω12)

Atejω=34

34=B(3412),B=3

 At ejω=1212=A(1234),A=2

Y(ejω)ejω=2ejω12+3ejω34

Y(ejω)=2ejωejω12+3ejωejω34

Applying IDTFT,

y(n)=2(12)nu(n)+3(34)nu(n)

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