Hello, I am reading the free DSP textbook from dspguide.com ( http://www.dspguide.com/pdfbook.htm ), and in chapter 2 on page 7, the author defines SNR as the mean divided by the standard deviation. This is the first time that I have seen SNR defined as such, and I do not see how it is consisten with the definition that I am familiar with, which Wikipedia.com gives as power ratio between a signal (meaningful information) and the background noisehttp://en.wikipedia.org/wiki/Signal-to-noise_ratio . Can anyone clear my confusion?? Thanks This message was sent using the Comp.DSP web interface on www.DSPRelated.com
Silly SNR question
Started by ●August 12, 2005
Reply by ●August 12, 20052005-08-12
sunshine wrote:> Hello, I am reading the free DSP textbook from dspguide.com ( > http://www.dspguide.com/pdfbook.htm ), and in chapter 2 on page 7, the > author defines SNR as the mean divided by the standard deviation. This is > the first time that I have seen SNR defined as such, and I do not see how > it is consisten with the definition that I am familiar with, which > Wikipedia.com gives as power ratio between a signal (meaningful > information) and the background > noisehttp://en.wikipedia.org/wiki/Signal-to-noise_ratio . > > Can anyone clear my confusion?? > > Thanks >I don't recall that I've ever seen SNR expressed in anything other than dB, which means that if you have it as a numerical ratio between signals then you'd automatically correct it into power notation when moving to dB... I'm not going to read that chapter just to answer a newsgroup question. If you have a constant signal, or one that's of much lower bandwidth than your integrating window, then dividing the measured mean by the measured standard deviation would give you a quite valid estimate of the SNR. Are you sure that this isn't what the author means, and either he didn't point this out or he did and you missed it? -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●August 12, 20052005-08-12
On Fri, 12 Aug 2005 07:33:51 -0700, Tim Wescott <tim@seemywebsite.com> wrote:>sunshine wrote: > >> Hello, I am reading the free DSP textbook from dspguide.com ( >> http://www.dspguide.com/pdfbook.htm ), and in chapter 2 on page 7, the >> author defines SNR as the mean divided by the standard deviation. This is >> the first time that I have seen SNR defined as such, and I do not see how >> it is consisten with the definition that I am familiar with, which >> Wikipedia.com gives as power ratio between a signal (meaningful >> information) and the background >> noisehttp://en.wikipedia.org/wiki/Signal-to-noise_ratio . >> >> Can anyone clear my confusion?? >> >> Thanks >> >I don't recall that I've ever seen SNR expressed in anything other than >dB, which means that if you have it as a numerical ratio between signals >then you'd automatically correct it into power notation when moving to dB... > >I'm not going to read that chapter just to answer a newsgroup question. > If you have a constant signal, or one that's of much lower bandwidth >than your integrating window, then dividing the measured mean by the >measured standard deviation would give you a quite valid estimate of the >SNR. Are you sure that this isn't what the author means, and either he >didn't point this out or he did and you missed it?Just to add a little to Tim's point: For many cases the OP has a legitimate concern as that statistical definition of SNR is not universal and doesn't always hold. The general definition of SNR is just the Signal power divided by the Noise power, and it is, as Tim stated, most often stated in dB. SNR = Signal to Noise Ratio = Signal/Noise Kinda follows from that, I'd hope. It's probably not beneficial to cloud that simple of a definition by the one you've just mentioned that you found online for a general case, so maybe the author was just pointing out something interesting for the special case. (I haven't read it, either.) Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org
Reply by ●August 13, 20052005-08-13
sunshine skrev:> Hello, I am reading the free DSP textbook from dspguide.com ( > http://www.dspguide.com/pdfbook.htm ), and in chapter 2 on page 7, the > author defines SNR as the mean divided by the standard deviation. This is > the first time that I have seen SNR defined as such, and I do not see how > it is consisten with the definition that I am familiar with, which > Wikipedia.com gives as power ratio between a signal (meaningful > information) and the background > noisehttp://en.wikipedia.org/wiki/Signal-to-noise_ratio . > > Can anyone clear my confusion??As others have said, stick with the general definition. As for the mean/variance definition I *believe* (I haven't read the book either) the definition just *might* make some sort of sense in the case of a constant (DC) signal and added noise. Except that I would have preferred to define the SNR as something like SNR = 10 * log_10 (mean^2/variance) So all in all, this might just be one of those cases where you got what you paid for when relying on a free book... Rune
Reply by ●August 14, 20052005-08-14
"Eric Jacobsen" <eric.jacobsen@ieee.org> wrote in message news:k23qf19ctqms96mmc6j65ruk86klu88fq1@4ax.com...> On Fri, 12 Aug 2005 07:33:51 -0700, Tim Wescott <tim@seemywebsite.com> > wrote: > >>sunshine wrote: >> >>> Hello, I am reading the free DSP textbook from dspguide.com ( >>> http://www.dspguide.com/pdfbook.htm ), and in chapter 2 on page 7, the >>> author defines SNR as the mean divided by the standard deviation. This >>> is >>> the first time that I have seen SNR defined as such, and I do not see >>> how >>> it is consisten with the definition that I am familiar with, which >>> Wikipedia.com gives as power ratio between a signal (meaningful >>> information) and the background >>> noisehttp://en.wikipedia.org/wiki/Signal-to-noise_ratio . >>> >>> Can anyone clear my confusion?? >>> >>> Thanks >>> >>I don't recall that I've ever seen SNR expressed in anything other than >>dB, which means that if you have it as a numerical ratio between signals >>then you'd automatically correct it into power notation when moving to >>dB... >> >>I'm not going to read that chapter just to answer a newsgroup question. >> If you have a constant signal, or one that's of much lower bandwidth >>than your integrating window, then dividing the measured mean by the >>measured standard deviation would give you a quite valid estimate of the >>SNR. Are you sure that this isn't what the author means, and either he >>didn't point this out or he did and you missed it? > > Just to add a little to Tim's point: For many cases the OP has a > legitimate concern as that statistical definition of SNR is not > universal and doesn't always hold. The general definition of SNR is > just the Signal power divided by the Noise power, and it is, as Tim > stated, most often stated in dB. > > SNR = Signal to Noise Ratio = Signal/Noise > > Kinda follows from that, I'd hope. It's probably not beneficial to > cloud that simple of a definition by the one you've just mentioned > that you found online for a general case, so maybe the author was just > pointing out something interesting for the special case. (I haven't > read it, either.) > > > Eric Jacobsen > Minister of Algorithms, Intel Corp. > My opinions may not be Intel's opinions. > http://www.ericjacobsen.orgWell, this is really a special case the author is talking about: "Before ending this discussion on the mean and standard deviation, two other terms need to be mentioned. In some situations, the mean describes what is being measured, while the standard deviation represents noise and other interference. In these cases, the standard deviation is not important in itself, but only in comparison to the mean. This gives rise to the term: signal-to-noise ratio (SNR), which is equal to the mean divided by the standard deviation." In other words, the "standard deviation" *is* the noise and the "mean" is the signal. Thus the "definition". Fred
Reply by ●August 14, 20052005-08-14
Fred Marshall <fmarshallx@remove_the_x.acm.org> wrote:>"Before ending this discussion on the mean and standard deviation, two other >terms need to be mentioned. In some situations, the mean describes what is >being measured, while the standard deviation represents noise and other >interference. In these cases, the standard deviation is not important in >itself, but >only in comparison to the mean. This gives rise to the term: signal-to-noise >ratio (SNR), which is equal to the mean divided by the standard deviation.">In other words, the "standard deviation" *is* the noise and the "mean" is >the signal. Thus the "definition".The mean (if by that we mean arithmetic mean) is only equal to the signal power for one type of signal -- a constant DC signal. The AC component of any signal has a mean of zero. So this is an exceptionally poor definition of SNR. Steve
Reply by ●August 14, 20052005-08-14
in article ddonam$n72$1@blue.rahul.net, Steve Pope at spope33@speedymail.org wrote on 08/14/2005 20:23:> Fred Marshall <fmarshallx@remove_the_x.acm.org> wrote: > >> "Before ending this discussion on the mean and standard deviation, two other >> terms need to be mentioned. In some situations, the mean describes what is >> being measured, while the standard deviation represents noise and other >> interference. In these cases, the standard deviation is not important in >> itself, but >> only in comparison to the mean. This gives rise to the term: signal-to-noise >> ratio (SNR), which is equal to the mean divided by the standard deviation." > >> In other words, the "standard deviation" *is* the noise and the "mean" is >> the signal. Thus the "definition". > > > The mean (if by that we mean arithmetic mean) is only equal > to the signal power for one type of signal -- a constant > DC signal. > > The AC component of any signal has a mean of zero. So this is > an exceptionally poor definition of SNR.i wouldn't give it the status of definition. maybe more the result of a particular known signal is of very low frequency content having very white or even high-pass noise added to it. out of the LPF would come something like a moving-mean, subtract that from a properly delayed input and get the AC component and compute the standard deviation from that. maybe it should be 10*log10(mean^2/variance). but it's no definition. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●August 15, 20052005-08-15
Well, at least I gave you a quote of what was being referred to. It's a pretty dumb "definition" if you ask me. As r-b-j notes: What if the noise is white noise - which is very often the case or at least for purposes of analysis - then the description given makes no sense. For example, desired signal of lowpass bandwidth 100Hz and total signal bandwidth of 500Hz. Now lowpass filter the signal to 100Hz. All we've done is remove the noise that's easy to remove. Noise up to 100Hz remains with the signal. I join in the recommendation to reject this "definition". Fred
Reply by ●August 15, 20052005-08-15
in article 1124121611.063854.248790@o13g2000cwo.googlegroups.com, Fred Marshall at fmarshall@acm.org wrote on 08/15/2005 12:00:> Well, at least I gave you a quote of what was being referred to. It's > a pretty dumb "definition" if you ask me. As r-b-j notes: > > What if the noise is white noise - which is very often the case or at > least for purposes of analysis - then the description given makes no > sense. For example, desired signal of lowpass bandwidth 100Hz and > total signal bandwidth of 500Hz. Now lowpass filter the signal to > 100Hz. All we've done is remove the noise that's easy to remove. > Noise up to 100Hz remains with the signal.i said that??? (capitalization should be a hint.)> I join in the recommendation to reject this "definition".it's not a definition, but i can think of some kinda scenario where 10*log10( variance/(mean)^2 ) could be the specific approximate result. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●August 15, 20052005-08-15
