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Measurements >> Other Measurements >> Query Signal to Noise Ratio of ADC
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Message started by shaikh_sarfraz on Sep 16^th, 2008, 10:56am

Title: Query Signal to Noise Ratio of ADC
Post by shaikh_sarfraz on Sep 16^th, 2008, 10:56am

Hi,
I am simulating an ADC for SNR.
I have got the frequency spectrum consisting of signal and noise.

Now as per definition SNR= 20*log(RMS_Signal/RMS_Noise)

RMS_Signal = Peak_Signal/sqrt(2)

My doubt is regarding calculating RMS_Noise:
Suppose I have 128 samples of noise
How is RMS_Noise defined:
1). temp = (Noise1)**2 + (Noise2)**2.........+(Noise128)**2
RMS_Noise = sqrt(temp/128)

2). temp = (Noise1)**2 + (Noise2)**2.........+(Noise128)**2
RMS_Noise = sqrt(temp/2)

Best Regards
Sarfraz

Title: Re: Query Signal to Noise Ratio of ADC
Post by Tlaloc on Sep 16^th, 2008, 8:20pm

It is most definitely #1. Remember that the M in RMS stands for mean. Standard mean is 1/N*(x₁+x₂+...+x_N). RMS is √(1/N*(x₁²+x₂²+...+x_N²)).

Quote:

RMS_Signal = Peak_Signal/sqrt(2)

This is only for the specific case when the signal is a sin wave.

Title: Re: Query Signal to Noise Ratio of ADC
Post by shaikh_sarfraz on Sep 17^th, 2008, 1:44am

Thanks for your reply.
If you go by RMS definition, then 1 should be the correct answer.
However I have seen, in many places (2) is being used.
So I wanted to make sure, which is the correct formulation.
It is my guess that is the noise sources are uncorelated than (2) should be used.

Can any body pour in more information?

Best Regards
Sarfraz

Title: Re: Query Signal to Noise Ratio of ADC
Post by Tlaloc on Sep 18^th, 2008, 12:45pm

Quote:

It is my guess that is the noise sources are uncorelated than (2) should be used.

Correlation has nothing to do with. RMS is still RMS. It is always the first definition when you have discrete points. If the signal is continuous, e.g. a sine wave, then the definition is 1/N*∫f(x)²dx. For the case of sine wave, the integral simplifies to sqrt(2)*peak.

Title: Re: Query Signal to Noise Ratio of ADC
Post by Tlaloc on Sep 22^nd, 2008, 7:56am

Sorry, the definition of the continuous time RMS was wrong. It should be 1/(T₂-T₁)*∫f(x)²dx with the integral taken from T₁ to T₂ for periodic functions. T₁ and T₂ needs to include an integer number of cycles.