For the sequences, determine the N-point:(a) Circular convolution x1(n)x2(n)(b) Circular...

Question

For the sequences, determine the N-point:(a) Circular convolution x1(n)x2(n)(b) Circular correlation of x1(n) and x2(n)(c) Circular auto correlation of x1(n)(d) Circular auto correlation ofx2(n)

Robert · Accepted Answer

(a) 
 
     
     
     
   
 
2 2
1
1
2
3 1 2
2
3
1
2
1 1
2
1 1
2
  
              1 1
4
2
              sin
2
n n
j j
N Nx n e e
N
X k k k
also
N
X k k k
j
So X k X k X k
N
k k
j
and
N n
x n
N
 
 
 
 

 
  
 
     
     

     
 
  
 
 
(b) 
     
   
 
1 2
2
         1 1
4
2
  sin
2
xy
xy
R k X k X k
N
k k
j
N n
r k
N
 


     
 
    
 
 
(c)
     
   
 
1 1
2
         1 1
4
2
  cos
2
xx
xx
R k X k X k
N
k k
N n
r k
N
 


     
 
   
 
 
(d) 
     
   
 
2 2
2
         1 1
4
2
  cos
2
yy
yy
R k X k X k
N
k k
N n
r k
N
 


     
 
   
 

For the sequences, determine the N-point: (a) Circular convolution x1(n)x2(n) (b) Circular correlation of x1(n) and x2(n) (c) Circular auto correlation of x1(n) (d) Circular auto correlation...

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