how do we arrive at the figure 6.02dB per bit? kavs
dynamic range per bit
Started by ●May 30, 2005
Reply by ●May 30, 20052005-05-30
aadhi wrote:> how do we arrive at the figure 6.02dB per bit? > kavsEvery added bit doubles the dynamic range. 3 bits have 8 states; 4 have 16. Can we take it from there? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 30, 20052005-05-30
"aadhi" <k.aadhivs@gmail.com> wrote in message news:1117454350.229506.51790@g43g2000cwa.googlegroups.com...> how do we arrive at the figure 6.02dB per bit? > kavs >It's a "rule of thumb", an approximation that gets closer to being true as the number of bits increases. Assuming that the collected bits represent voltage or current (or something else that you have to square to compute power) and that E1 and E2 both have some "reasonable" number of bits (like 7 and 8): (P1/P2) = 10*log10((E1/E2)**2) = 20*log10(E1/E2). In this case, if E1 has one more bit than E2, then maximum number represented by E1 is about twice the maximum number represented by E2 and, if they're both scaled the same, then the maximum value of E1/E2 is about 2. Then, as a result of extending E1 by one bit, the ratio of powers you can represent relative to E2 is: (P1/P2) = 20*log10(2) = 6.02 dB (per bit). In our example, we said E1 had 8 bits and E2 had 7 bits. Well (P1/P2) = 20*log10(255/127) = 20*log10(2.008) = 6.05 dB. With 12 or 16 bits, the approximation is very close.
Reply by ●May 30, 20052005-05-30
in article I4Gme.39213$lQ3.11030@bignews5.bellsouth.net, John E. Hadstate at jh113355@hotmail.com wrote on 05/30/2005 11:20:> It's a "rule of thumb", an approximation that gets closer to > being true as the number of bits increases.it's not a (empirical) rule of thumb. if you fix the definition of the signal and noise (noise will be the uniform PDF roundoff error) and the amount of headroom, no matter how you define it, as long as it's consistent, then when you define dynamic range as dB of S/N + dB of headroom, you get exactly 20*log10(2) ~= 6.02 dB increase each time you add a bit. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●May 30, 20052005-05-30
"robert bristow-johnson" <rbj@audioimagination.com> wrote in message news:BEC0B37F.7C0B%rbj@audioimagination.com...> in article I4Gme.39213$lQ3.11030@bignews5.bellsouth.net, > John E. Hadstate at > jh113355@hotmail.com wrote on 05/30/2005 11:20: > >> It's a "rule of thumb", an approximation that gets closer >> to >> being true as the number of bits increases. > > it's not a (empirical) rule of thumb. if you fix the > definition of the > signal and noise (noise will be the uniform PDF roundoff > error) and the > amount of headroom, no matter how you define it, as long > as it's consistent, > then when you define dynamic range as dB of S/N + dB of > headroom, you get > exactly 20*log10(2) ~= 6.02 dB increase each time you add > a bit. >Quite simply, you don't know what you're talking about and you're babbling nonsense. Are you drunk, or are you a moron?
Reply by ●May 30, 20052005-05-30
On Mon, 30 May 2005 14:17:35 -0400, "John E. Hadstate" <jh113355@hotmail.com> wrote:> >"robert bristow-johnson" <rbj@audioimagination.com> wrote in >message news:BEC0B37F.7C0B%rbj@audioimagination.com... >> in article I4Gme.39213$lQ3.11030@bignews5.bellsouth.net, >> John E. Hadstate at >> jh113355@hotmail.com wrote on 05/30/2005 11:20: >> >>> It's a "rule of thumb", an approximation that gets closer >>> to >>> being true as the number of bits increases. >> >> it's not a (empirical) rule of thumb. if you fix the >> definition of the >> signal and noise (noise will be the uniform PDF roundoff >> error) and the >> amount of headroom, no matter how you define it, as long >> as it's consistent, >> then when you define dynamic range as dB of S/N + dB of >> headroom, you get >> exactly 20*log10(2) ~= 6.02 dB increase each time you add >> a bit. >> > >Quite simply, you don't know what you're talking about and >you're babbling nonsense. Are you drunk, or are you a >moron?No, he's just right. The analysis that rb-j just referenced is very well understood and can be found in ADC/DAC data sheets and white papers from companies like TI and ADI as well as many text books. What part of it do you disagree with? Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org
Reply by ●May 30, 20052005-05-30
in article YGIme.39697$lQ3.36220@bignews5.bellsouth.net, John E. Hadstate at jh113355@hotmail.com wrote on 05/30/2005 14:17:> "robert bristow-johnson" <rbj@audioimagination.com> wrote in > message news:BEC0B37F.7C0B%rbj@audioimagination.com... > >> in article I4Gme.39213$lQ3.11030@bignews5.bellsouth.net, >> John E. Hadstate at jh113355@hotmail.com wrote on 05/30/2005 11:20: >> >>> It's a "rule of thumb", an approximation that gets closer >>> to being true as the number of bits increases. >> >> it's not a (empirical) rule of thumb. if you fix the definition of the >> signal and noise (noise will be the uniform PDF roundoff error) and the >> amount of headroom, no matter how you define it, as long as it's consistent, >> then when you define dynamic range as dB of S/N + dB of headroom, you get >> exactly 20*log10(2) ~= 6.02 dB increase each time you add a bit. >> > > Quite simply, you don't know what you're talking about and > you're babbling nonsense. Are you drunk, or are you a moron?:-) at least we know it ain't "The Ghost". -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●May 30, 20052005-05-30
Eric Jacobsen wrote:> On Mon, 30 May 2005 14:17:35 -0400, "John E. Hadstate" > <jh113355@hotmail.com> wrote: > > >>"robert bristow-johnson" <rbj@audioimagination.com> wrote in >>message news:BEC0B37F.7C0B%rbj@audioimagination.com... >> >>>in article I4Gme.39213$lQ3.11030@bignews5.bellsouth.net, >>>John E. Hadstate at >>>jh113355@hotmail.com wrote on 05/30/2005 11:20: >>> >>> >>>>It's a "rule of thumb", an approximation that gets closer >>>>to >>>>being true as the number of bits increases. >>> >>>it's not a (empirical) rule of thumb. if you fix the >>>definition of the >>>signal and noise (noise will be the uniform PDF roundoff >>>error) and the >>>amount of headroom, no matter how you define it, as long >>>as it's consistent, >>>then when you define dynamic range as dB of S/N + dB of >>>headroom, you get >>>exactly 20*log10(2) ~= 6.02 dB increase each time you add >>>a bit. >>> >> >>Quite simply, you don't know what you're talking about and >>you're babbling nonsense. Are you drunk, or are you a >>moron? > > > No, he's just right. > > The analysis that rb-j just referenced is very well understood and can > be found in ADC/DAC data sheets and white papers from companies like > TI and ADI as well as many text books. What part of it do you > disagree with?I think Hadstate has fallen into the n - 1 trap (discounting the sign bit), counting only 2**(n - 1) states for n bits. If so, he can find his error for himself; I try not to associate with his likes. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 30, 20052005-05-30
robert bristow-johnson wrote:> > :-) > > at least we know it ain't "The Ghost". >At least we're sure who you are. Your turkey-attractor is still in fine form. ;-) Ciao, Peter K.
Reply by ●May 30, 20052005-05-30
"Eric Jacobsen" <eric.jacobsen@ieee.org> wrote in message news:6aqm911dbsjpvrjui5e3g5uetqsn6qu8dh@4ax.com...> On Mon, 30 May 2005 14:17:35 -0400, "John E. Hadstate" > <jh113355@hotmail.com> wrote: > >> >>"robert bristow-johnson" <rbj@audioimagination.com> wrote >>in >>message news:BEC0B37F.7C0B%rbj@audioimagination.com... >>> in article I4Gme.39213$lQ3.11030@bignews5.bellsouth.net, >>> John E. Hadstate at >>> jh113355@hotmail.com wrote on 05/30/2005 11:20: >>> >>>> It's a "rule of thumb", an approximation that gets >>>> closer >>>> to >>>> being true as the number of bits increases. >>> >>> it's not a (empirical) rule of thumb. if you fix the >>> definition of the >>> signal and noise (noise will be the uniform PDF roundoff >>> error) and the >>> amount of headroom, no matter how you define it, as long >>> as it's consistent, >>> then when you define dynamic range as dB of S/N + dB of >>> headroom, you get >>> exactly 20*log10(2) ~= 6.02 dB increase each time you >>> add >>> a bit. >>> >> >>Quite simply, you don't know what you're talking about and >>you're babbling nonsense. Are you drunk, or are you a >>moron? > > No, he's just right. > > The analysis that rb-j just referenced is very well > understoodrjb didn't do any analysis. He merely spouted forth some pseudo-technical gibberish. If you don't know the difference, and I suspect you don't, you're no more than a troll's Greek chorus.
