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Find response of system using DTFT, h(n)=(12)nu(n);x(n)=(34)nu(n)
1 Answer
written 2.3 years ago by |
Solution:
h(n)=(12)nu(n);x(n)=(34)nu(n)
H(ejω)=11−12e−jω;X(ejω)=11−34e−jωY(ejω)=H(ejω)X(ejω)
Y(ejω)=11−12e−jω⋅11−34e−jω=ejωejω−12⋅ejωejω−34Y(ejω)ejω=ejω(ejω−12)(ejω−34)=Aejω−12+Bejω−34ejω=A(ejω−34)+B(ejω−12)
Atejω=34
34=B(34−12),∴B=3
At ejω=1212=A(12−34),∴A=−2
Y(ejω)ejω=−2ejω−12+3ejω−34
Y(ejω)=−2ejωejω−12+3ejωejω−34
Applying IDTFT,
y(n)=−2(12)nu(n)+3(34)nu(n)