# Signal to Noise ratio dB levels

1. Sep 23, 2011

### rama1001

Hello,
I have some 10 signals in noisy and nonoise(noisy+good) situations. I just calculated the power of each signal in two cases and then used SNR formula for dB(10log noisy/nonoise).

Now, I got noise levels in dB's. Here, i confused that these dB levels are refered to sound dB levels or some other dB's. Because, My teacher told me after seeing the achieved values(20dB, 32dB, 14dB......upto 10 signal values) and he said it was full noisy.

I am pointing here that what is these dB values and is there any chart for good and bad noise dB values or any information about this is appriciated.

2. Sep 23, 2011

### Floid

A few points.

DB measurements:

In general, dB measurements are ratios (and in the application you listed they always are). So if you have a dB measurement that was 10dB that means that you had one thing that was some amount greater than the other. For SNR you are measuring the ratio of two powers so you use the equation 20*log10(x/y) which means that if you had a 10dB difference, x was 10x greater than y or if you had 20dB difference then x was 100x greater than y etc. The 20 comes from the fact that your actual equation is 10*log10(x^2/y^2) where x and y are signal amplitudes but you can pull out the square using the properties of logarithms.

At other times dBs are used to give strength relative to something. For example dBm is commonly used for transmission powers and this is decibals relative to a milliWatt. So in this case you use 10*log10(x/1mW). The y term from above is always fixed and the number you get gives you an idea of scale of how much stronger or weaker the signal is relative to a mW.

On SNR:

As I explained above the typical SNR equation is 20*log10(signal power/noise power). From what you stated above I wasn't sure if you were clear on that. To estimate the noise power you either have to measure it, make assumptions about it, or try to extract it if you have clean signal and then signals with noise.

What is a good SNR to ratio? That depends on your system and the amount of noise you can tolerate. For digital systems you can use SNR to calculate your bit error rate (BER). Usually for a given system you establish what an acceptable BER is and then work backwards to what your SNR needs to be and that tells you what you need to do in that signal's transmission.

For analog signals you also have to consider the application in a somewhat similar manner.

Last edited: Sep 23, 2011
3. Sep 23, 2011

### rama1001

Sorry for the wrong information, I forgot that i used 20log(p1/p2). Thank you so much for such a good explanation.

4. Sep 23, 2011

### skeptic2

Shouldn't it be 10*log10(signal power/noise power) or 20*log10(signal voltage/noise voltage)?