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

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To determine the RMS amplitude of a sinusoidal signal in a noisy environment, the relationship between signal-to-noise ratio (SNR) and RMS values is crucial. Given an RMS noise value of 0.5 volts and an SNR of 10 dB, the correct calculation leads to an RMS amplitude of 1.58 volts. However, further discussion reveals that the expected answer should actually be 10 volts, indicating a potential misunderstanding of the SNR formula. Clarification on the relationship between the signal and noise is needed for accurate results. Understanding these concepts is essential for tackling similar problems in the future.
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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