sm9_12

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Problem 9.12 Evaluate the autocorrelation function of the in-phase and quadrature 
components of narrowband noise at the coherent detector input for the DSB-SC system. 
Assume the band-pass noise spectral density is SN(f) = N0/2 for |f-fc| < BT. 
 
Solution 
From Eg. (8.98), the in-phase power spectral density is (see Section 8.11) 
 
 
( )
( ) ( )
0
( )
/ 2
0 o
/ 2
0 otherwise
I QN N
N c N c T
T
S f S f
S f f S f f f B
N f B
=
⎧ − + + <⎪= ⎨⎪⎩
⎧ <⎪= ⎨⎪⎩
therwise 
 
From Example 8.13, the autocorrelation function corresponding to this power spectral 
density is 
 
 ( ) ( ) ( )0 sincQ IN N TR R N B BTτ τ τ= = 
 
 
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