What Is the RMS Amplitude of a Sinusoid in a Noisy Environment?

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SUMMARY

The discussion centers on calculating the RMS amplitude of a sinusoidal signal in a noisy environment, given an RMS noise value of 0.5 volts and a signal-to-noise ratio (SNR) of 10 dB. The equation used is SNR = 20 log(signal/noise). The correct RMS amplitude of the sinusoid is determined to be 1.58 volts, which aligns with the SNR calculation. However, a participant suggests that the answer should be exactly 10 volts, indicating a potential misunderstanding or missing relationship in the calculations.

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TomUIC
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Q: A single sinusoidal signal is found in a large amount of noise. If the RMS value of the noise is 0.5 volts and the SNR is 10 dB, what is the RMS amplitude of the sinusoid?

I've related the question to the following equation: SNR=20log(singal/noise)dB

My answer is 1.58 volts, BUT I'm not entirely sure if that is what they are asking for. Just looking for a little guidance on the question.
 
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Hi TomUIC. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

20.log(1.58/0.5) = 10 dB so your answer looks right. :smile:
 
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Hmmmm ... the answer is exactly 10 ... homework?
 
Windadct said:
Hmmmm ... the answer is exactly 10 ... homework?

Yes homework, what relationship am I missing? I'm new to this area so any help is appreciated.
 

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