Consider a finite-duration sequence x(n), 0 = n = 7, with z-transform X(z). We wish to compute X(z)...

Question

Consider a finite-duration sequence x(n), 0 = n = 7, with z-transform X(z). We wish to compute X(z) at the following set of values:
zk = 0.8ej[(2pk/8)+(p/8)] 0 = k = 7
(a) Sketch the points {zk} in the complex plane.
(b) Determine a sequence s(n) such that its DFT provides the desired samples of X(z).

David · Accepted Answer

(a) 
2
60.8
k
j
n
kZ e
  
 
   
(b)
   
 
   
27
6
0
27
6
0
        0.8
  0.8
kz z
n
k
j
n
n
n
k
j
n
n
X k X z
x n e
s n x n e
 
 


 
 
 


 
 
 


 
  
  
 
  
  



Consider a finite-duration sequence x(n), 0 = n = 7, with z-transform X(z). We wish to compute X(z) at the following set of values: zk = 0.8ej[(2pk/8)+(p/8)] 0 = k = 7 (a) Sketch the points {zk} in...

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