sm9_9
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sm9_9


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Problem 9.9 A sample function 
 
)()2cos()( twtfAtx cc += \u3c0 
 
is applied to a low-pass RC filter. The amplitude Ac and frequency fc of the sinusoidal 
component are constant, and w(t) is white noise of zero mean and power spectral density 
N0/2. Find an expression for the output signal-to-noise ratio with the sinusoidal 
component of x(t) regarded as the signal of interest. 
 
Solution 
The noise variance is proportional to the noise bandwidth of the filter so from Example 
8.16, 
 
( )[ ] 002 4 1 NRCNBtn N ==E 
 
and the signal power is fir a sinusoid, so the signal-to-noise ratio is given by 2/2cA
 
0
2
0
2 2
4
2 N
RCA
RC
N
ASNR cc =
\u239f\u23a0
\u239e\u239c\u239d
\u239b= 
 
 
 
 
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