"Jerry Avins" <jya@ieee.org> wrote in message news:3F0EDB9D.BD2E5E6F@ieee.org...> Glen Herrmannsfeldt wrote: > > > > ... uniform spacing minimizes the effect of quantization error.I can think of a number of different ways to say it, so ... For uniform sample spacing, the effect of any error in the sample value on the reconstructed signal is no larger than the error. If you consider the reconstructed signal as sinc()s it will be the error multiplied by sinc(). As the sample spacing gets less and less uniform the effect of errors on the reconstructed signal increases. Consider a signal defined over [0,T), but with all the sample points between 0 and T/2, though still T Fn points. Mathematically, that is enough information to reconstruct the signal. The reconstruction between T/2 and T is very sensitive to errors in the sample points. Another way to consider it is as an inverse of a less well conditioned matrix multiplied by the sample values. Small errors in the samples can generate large errors in the reconstruction. -- glen
Non uniform sampling
Started by ●July 9, 2003
Reply by ●July 11, 20032003-07-11
Reply by ●July 11, 20032003-07-11
Glen Herrmannsfeldt wrote:> > "Jerry Avins" <jya@ieee.org> wrote in message > news:3F0EDB9D.BD2E5E6F@ieee.org... > > Glen Herrmannsfeldt wrote: > > > > > > ... uniform spacing minimizes the effect of quantization error. > > I can think of a number of different ways to say it, so ... > > For uniform sample spacing, the effect of any error in the sample value on > the reconstructed signal is no larger than the error. If you consider the > reconstructed signal as sinc()s it will be the error multiplied by sinc(). > > As the sample spacing gets less and less uniform the effect of errors on the > reconstructed signal increases. > > Consider a signal defined over [0,T), but with all the sample points between > 0 and T/2, though still T Fn points. Mathematically, that is enough > information to reconstruct the signal. The reconstruction between T/2 and T > is very sensitive to errors in the sample points. > > Another way to consider it is as an inverse of a less well conditioned > matrix multiplied by the sample values. Small errors in the samples can > generate large errors in the reconstruction. > > -- glenGotcha! Another way to put it is that those clever schemes for squeezing information from clustered samples, determining the frequency on a signal known to be a single sinusoid, and computing with high-order derivatives all require fantastically high SNRs, and that it doesn't take very much for quantization "noise" to swamp the boat. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
