Hello! I am newbee in DSP and am reading the book by Steven Smith. In chapter three, the PDF of quantization error is not a gaussian. And I am wondering why? The errors are random then why isn't it a gaussian? Can somebody help me on this? Thanx in advance Regards --Himanshu

# PDF of Quantization Error

Started by ●December 31, 2004

Reply by ●December 31, 20042004-12-31

hschauhan wrote:> Hello! > > I am newbee in DSP and am reading the book by Steven Smith. In chapter > three, > the PDF of quantization error is not a gaussian. And I am wondering > why? > The errors are random then why isn't it a gaussian? > Can somebody help me on this? > > Thanx in advanceWhat makes you believe that ever random distribution is Gaussian? That's clearly not even approximately true. Most simple pseudo-random number generators have uniform distributions, as does an honest roulette wheel. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������

Reply by ●December 31, 20042004-12-31

hschauhan wrote:> Hello! > > I am newbee in DSP and am reading the book by Steven Smith. In chapter > three, > the PDF of quantization error is not a gaussian. And I am wondering > why? > The errors are random then why isn't it a gaussian? > Can somebody help me on this? > > Thanx in advance > > Regards > --Himanshu >If I take a coin and assign a value of 1 to heads and -1 to tails, and flip the coin, the PDF of the resulting value is not Gaussian. Why? The coin flips are random, why isn't the PDF a Gaussian? If I take the instantaneous power of a random process with a zero-mean Gaussian distribution the resulting PDF is Rayleigh, not Gaussian. Why? The instantaneous power is random, why isn't it's PDF Gaussian? If I look at the PDF of the values of a low-light detector that only collects a few photons each sampling period it's PDF is not Gaussian. Why? The process is random (it's a Poisson, by the way), why isn't it's PDF Gaussian? Answer these questions, and you will have a very good start on answering yours. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com

Reply by ●December 31, 20042004-12-31

Hi! I think it is because of the uniform distribution of the QEs. It is not gaussian because the probablity of occurence is same. Am I true? Regards --Himanshu

Reply by ●December 31, 20042004-12-31

hschauhan wrote:> Hi! > > I think it is because of the uniform distribution of the QEs. It is not > gaussian > because the probablity of occurence is same. > Am I true? > > Regards > --Himanshu >Yes, that is correct. Jerry's point (and mine, for that matter), was that you have no cause to be surprised that a particular PDF is not Gaussian. In fact, I suspect that there are very few, if any, underlying processes that actually have PDF's that are Gaussian if you dig deep enough. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com

Reply by ●December 31, 20042004-12-31

Tim Wescott wrote:> hschauhan wrote: > >> Hello! >> >> I am newbee in DSP and am reading the book by Steven Smith. In chapter >> three, >> the PDF of quantization error is not a gaussian. And I am wondering >> why? >> The errors are random then why isn't it a gaussian? >> Can somebody help me on this? >> >> Thanx in advance >> >> Regards >> --Himanshu >> > If I take a coin and assign a value of 1 to heads and -1 to tails, and > flip the coin, the PDF of the resulting value is not Gaussian. Why? The > coin flips are random, why isn't the PDF a Gaussian? > > If I take the instantaneous power of a random process with a zero-mean > Gaussian distribution the resulting PDF is Rayleigh, not Gaussian. Why? > The instantaneous power is random, why isn't it's PDF Gaussian? > > If I look at the PDF of the values of a low-light detector that only > collects a few photons each sampling period it's PDF is not Gaussian. > Why? The process is random (it's a Poisson, by the way), why isn't it's > PDF Gaussian? > > Answer these questions, and you will have a very good start on answering > yours.Just as Gaussian is the limiting case of binomial, Rayleigh is the limiting case of Poisson. That insight has served me well a few times. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������

Reply by ●December 31, 20042004-12-31

The distribution of the QE is related the distribution of the input signal. But we can conclude that this distribution must not be Gasssian strictly because the QE can't reach the infinity while Gassian random variable will do. Gassian is regular is part becasue the central limited theorem. But here if the input signal is uniform distribution, I can't see any reasion that the output QE is Gaussian distribution. and Yes ,as had beed said as above, it helps that you think about the physical meaning of some mathematic assumption.

Reply by ●January 1, 20052005-01-01

"Jerry Avins" <jya@ieee.org> wrote in message news:33lmu9F40e1dsU1@individual.net...> hschauhan wrote: > > > Hello! > > > > I am newbee in DSP and am reading the book by Steven Smith. In chapter > > three, > > the PDF of quantization error is not a gaussian. And I am wondering > > why? > > The errors are random then why isn't it a gaussian? > > Can somebody help me on this? > > > > Thanx in advance > > What makes you believe that ever random distribution is Gaussian? That's > clearly not even approximately true. Most simple pseudo-random number > generators have uniform distributions, as does an honest roulette wheel. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �If you use the central limit theorem everything is Guassian eventually!

Reply by ●January 1, 20052005-01-01

Hi!! I also think that more the random components, more is the Gaussian nature. Because random ness of all forces change the distribution from uniform to normal one. is that right? Regards --Himanshu

Reply by ●January 1, 20052005-01-01

Country_Chiel wrote:> "Jerry Avins" <jya@ieee.org> wrote in message...>>What makes you believe that ever random distribution is Gaussian? That's >>clearly not even approximately true. Most simple pseudo-random number >>generators have uniform distributions, as does an honest roulette wheel. > > > If you use the central limit theorem everything is Guassian eventually!Most (but not all) distributions become Gaussian when enough instances are summed. No matter how long you wait for the typical PRNG to exhibit a Gaussian distribution, your "eventually" will never come. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������