# Talk:Signal-to-noise ratio

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## SNR for various modulation systems

What is meaning of A_c W N_0 etc in formula? — Preceding unsigned comment added by 210.94.41.89 (talk) 07:25, 10 August 2012 (UTC)

## Initial comment

Information theory has been around since 1948; telecommunications much longer, and usenet only since the '80s. So "signal-to-noise ratio" cannot have originated in usenet. 131.183.81.100 01:58 Mar 4, 2003 (UTC)

## What does this mean?

In the article, this was placed without context:

• In Audio Coding there are terms like

These links don't really go anywhere or appear to be much use, so I removed them. --Twinxor 04:07, 12 May 2005 (UTC)

## What's better?

What's better? A high or a low SNR? Maybe someoine can give the formula for calculating SNR? Thanks, --Abdull 10:01, 21 May 2005 (UTC)

Generally, a high SNR is desirable since the signal is defined to be something of interest. I'm hard pressed to think of an example when one would desire a very low SNR (no signal, only noise).

- This is just the case I am working on. In smoothing algorithms "signal" is a second derivative jump due to data, it could be transferred to "noise" component. The trade-off between "noise" and "signal" in that case requies understanding of "what is level of non-recongnizable signal" (193.167.195.60 11:06, 14 March 2007 (UTC)).

The best I can do is if you interpret the channel as an encrypted one where the signal is the unencrypted data....then you would want the "viewer" to see as much "noise" as possible so they can't "see" the unencrypted data.  But, generally, the higher the SNR the better.

As for the formula, it can vary slightly. Generally:
$SNR = \frac{P_{signal}}{P_{noise}}$
which is the ratio of powers of the signal and the noise. Cburnett 20:42, May 24, 2005 (UTC)

## Associated Page may crash your PC

Modern PC, plenty of memory using Internet Explorer 6.0. PC crashed about where the second formula is.

Can edit the page OK - but don't know enough to work out why I got a blue screen of death. This occurred on a colleagues PC, so is repeatable (older PC but same vsn of IE).

Help?

## Digital SNR derivation

As far as I know, 6*n dB is an approximation. Also, the formula listed contradicts itself:

$\mathrm{SNR} = 10(2n-1) \cdot \log_{10}(2)+10 \cdot 3 = 6.02 \cdot n + 26.989$

not $6.02 \cdot n + 1.763$

This PDF has a different derivation:

$\mathrm{SNR} = 2^n ( {\sqrt {3} / \sqrt{2}} )$
$\mathrm{SNR_{dB}} = 20 \log_{10} \left ( 2^n ( {\sqrt {3} / \sqrt{2}} ) \right )$
$\mathrm{SNR_{dB}} = 20 \log_{10} ( 2) \cdot n + 20 \log_{10} ( \sqrt {3} / \sqrt{2})$
$\mathrm{SNR_{dB}} = 6.021 n + 1.763$Omegatron 15:13, August 30, 2005 (UTC)
Thanks for fixing the formula, User:212.119.9.186!
With more precision is 6.020599 n + 1.760913, if it matters. — Omegatron 15:49, 10 October 2005 (UTC)
Also, $10(2n-1) \cdot \log_{10}(2)+10\log_{10}(3) = 20 \log_{10} ( 2) \cdot n + 20 \log_{10} ( \sqrt {3} / \sqrt{2})$Omegatron 01:20, 11 October 2005 (UTC)

Ok, the 6.02n formula corresponds to a noise level caused by a uniform fluctuation between two quantization levels. I think another way of saying this is that the sampled value is assumed to be uniformly distributed across the possible range of values.

The 6.02n+1.761 formula maybe only applies to the ratio of a full-scale sine wave to the error signal, as hinted at in the article? So the signal is assumed to be a sine wave instead of being unknown but uniformly distributed. I will try to do the math later.

Is there another for a Gaussian distribution? — Omegatron 17:32, 30 November 2005 (UTC)

As I've explained in the article, the noise is signal-dependent, so SNR for a system requires that you come up with a model of what that signal is going to look like first. — Omegatron 20:25, 12 March 2006 (UTC)
RMS signal = $A \over \sqrt{2}$ or $FSR/2 \over \sqrt{2}$ where FSR is the full-scale range of the converter
RMS noise = $q \over \sqrt{12}$ where q is the LSB

### A million different equivalent equations

• $10(2n-1) \cdot \log_{10}(2)+10\log_{10}(3)$
• $20 \log_{10}(2^{n-1} \sqrt{6})$[1]
• $20 \log_{10} \left ( {2^n \sqrt{12} \over 2 \sqrt{2}} \right )$[2]
• $20 \log_{10} ( 2) \cdot n + 20 \log_{10} ( \sqrt {3} / \sqrt{2})$[3]
• $2n\cdot10\log_{10}(2)+10\log_{10}(3/2)$ Totally forgot we have a derivation over at Talk:Quantization_noise#ThesisOmegatron 02:35, 13 March 2006 (UTC)

## SNR = 8 sigma ... what does the sigma mean?

Nasa describes the performance of a CCD in a space-based optical telescope as having SNR = 8 Sigma

I'm sure someone can explain to me if this just means SNR is 10^8? Or what does it mean?

-Kevin

I'm not exactly sure, but sigma often refers to standard deviation, so my guess would be that this means that the SNR is equivalent to (1/) 8 standard deviations in a gaussian distribution or 6x10^-16 or 150dB. This is of course unfounded conjecture, use at your own risk (this corresponds to 25bits, which seems dubious)

## SNR

How can I calculate the SNR for video quality? sorry about my spelling

## Different meanings of SNR

The current article focusses on the SNR of sound. However, there are alternative meanings and definitions for the SNR, such as for analytical instruments. For instruments, the SNR (signal intensity / standard deviation of background) is a measure for the quality of the signal: if the SNR for a signal is less dan 3, it is not detected, whereas if it is higher than 10, the signal can be quantified. See also the SNR on the Dutch wikipedia. Therefore, I suggest to adapt the article or write a new completely new one. Annabelleke 13:56, 15 March 2007 (UTC)

Nonsense; there is only one definition of SNR (except that in video and image the definition gets perverted somewhat by common usage), and it has nothing specific to sound; the dB scale is commonly used for all sorts of sound and non-sound signals, but is completely optional. And detection thresholds are not so simple as you say. Dicklyon 23:34, 15 March 2007 (UTC)
Yeah, OK. There's is indeed only one definition (cfr. introduction of the article), but it is expressed in different ways for different disciplines. Therefore, there should be at least a paragraph or notion on the different expressions of definition. In many disciplines, in fact in most disciplines, people don't speak of the power of power ratio. This term comes from fourier transform analysis of a signal.
In addition, in the case of analytical chemistry, e.g. for spectroscopic measurements, detection limit is defined, by making use of the SNR.
Annabelleke 08:02, 16 March 2007 (UTC)
Please do add info about that. Actually, I'm no longer sure of the definition in terms of power ratio, since the SNR is often quantified as an amplitude ratio; either way, one article should cover it all. Need to review some books... Dicklyon 08:18, 16 March 2007 (UTC)

## SNR in image processing

The article says "In image processing, the SNR of an image is usually defined as the ratio of the mean pixel value to the standard deviation of the pixel values" but that sounds confusing to me. I guess it involves time series (thus every pixel in a static image is acquired several times, and its standard deviation can be assigned to noise) or a constant (homogeneous) image; but the way it's written suggests that the standard deviation is calculated over all the pixels in a single frame image, whatever it is. The latter is of course false: the variability of different pixels in an image can be due to the object being imaged, and not all of it is just noise. Default007 13:40, 14 August 2007 (UTC)

## "unreferenced driveby edit"

I, too, usually just revert small uncommented changes to new or anonymous editors. But in this case, the removal of the square from the amplitude ratio was correct. It's taken care of by the 20 instead of 10 multiplying the log of the ratio. Editors, please use edit summaries to tell us what your edit is about, so it can be distinguished from drive-by vandalism. Dicklyon 14:50, 17 October 2007 (UTC)

## NPR

At NPR (disambiguation), someone had added an entry for Noise Power Ratio, though we don't seem to have such a page. It seems to me that this should probably redirect (if at all) to here, Signal-to-noise ratio. Do other editors agree? Or is a separate page needed? References are here:[4][5] Thanks, Elonka 04:02, 16 May 2008 (UTC)

In books, it does seem to be a genuine term and acronym. Better read some of those books and see what it means. Dicklyon (talk) 05:31, 16 May 2008 (UTC)

## Good level

What's good; anything over 100. Is 105 dB good? Daniel Christensen (talk) 15:29, 29 April 2009 (UTC)

A 100 dB SNR would be exceptionally high, and very unusual; hard to imagine even, in any kind of sound or image system. Speech is easily intelligible at 0 dB SNR, and perfectly intelligible at 20 dB, and sounds very clean at 40 dB. So what do you mean by good? For what? Dicklyon (talk) 19:56, 29 April 2009 (UTC)
Damaging your hearing, maybe. Atypicaloracle (talk) 14:06, 10 June 2010 (UTC)
It's common in audio analysis to treat 60 dB as roughly-as-good-as-silent, e.g. when analysing how long reverb lasts. --mcld (talk) 11:07, 3 January 2013 (UTC)

SINAD is a variant on Signal-to-noise ratio with total signal (as opposed to wanted signal) in the numerator. The concept is the same. The math is slightly different. I think it would be more efficient to cover both in the same article. -—Kvng 14:00, 21 December 2012 (UTC)

• Merge as proposed. Binksternet (talk) 14:24, 21 December 2012 (UTC)
• Oppose: the SNR article is already long enough, the SINAD article has plenty of content, and it appears that SINAD is a concept referred to enough by certain engineers that it's not a trivial variant. --mcld (talk) 11:05, 3 January 2013 (UTC)
• Oppose: SINAD is a slightly different concept, and the current SINAD article has enough content. GyroMagician (talk) 14:36, 10 February 2013 (UTC)
Unless the resulting merged article would be too long, I don't think the length of the existing articles is pertinent to a merge decision. I don't think it makes sense to have a separate article on a topic which is "slightly different". -—Kvng 18:15, 13 February 2013 (UTC)
Maybe I should phrase my comment slightly differently then. Look at the ratios section in the noise box at the bottom of the article. Should all of these ratios be merged into the SNR article? I don't think so. Most users of SNR have never heard of SINAD (I certainly hadn't until I found it on WP). It's a very specific, well-defined term, used by a relatively small group. I do think length is important - if the SINAD page was a single line, I'd agree to merge it here, but I think the article stands in its own right, which is why I oppose the merge. I don't see a persuasive argument to merge. GyroMagician (talk) 16:42, 15 February 2013 (UTC)
I've looked in both articles and I can't find the noise box of which you speak. -—Kvng 15:07, 17 February 2013 (UTC)
Sorry, I should have been clearer. I mean the box with all the links to noise-related articles, found at the bottom of the page. You can also see it here: Template:Noise GyroMagician (talk) 09:21, 18 February 2013 (UTC)
Thanks for the context. Doesn't look like a merge is a good idea. I have taken down the banners. -—Kvng 17:17, 20 February 2013 (UTC)

This article presents formula parameter symbols for channel and output S/N for AM and FM modulation that are not defined.

## Biochemical Signalling between cells

I came to this page for information on what SNR meant in the context of intercellar signalling. It's mentioned in the opening paragraph but not expanded upon later on in the article. The link provided in the first paragraph doesn't refer to SCN either. Might it be useful to include info on how SCN is manifest in biochemical signalling?