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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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