adamdea;582294 Wrote: > Thanks. This is very helpful too. > I am afraid that having got my tiny mind a little way into this problem > a couple of weeks ago, I then got too distracted by the tedious business > of earning a living etc to pose the next incisive question which I have > now forgotten. > I realised at about the same time that the area where i migth be > getting my knickers in a twist was not in the mathematical properties > of binary numbers but the way that noise works in an electrical > system. > What you have said about the noise floor very elegantly illustrates a > confusion i had had about whether the noise floor would always be added > to the signal in an analog system or whether it could ever be > swamped.(ie cease to have any impact at all when the signal was strong > enough.) I understand the answer to be "no". > > It seems that the range of amplitude values expressed by an analog > system should be perfectly reproducible by a digital system with > dither added, provided that the digital system had sufficent resoltuion > to resolve a noise below the noise floor of the analog system. > > > I wonder whether the ruler analogy a breaks down though once one looks > at a sequence of samples. It occurs to me that if the noise is random > then one could still in principle detect the difference between two > signals the difference between which is lower than the noise floor. > [Please forgive me if I have got the wrong end of the stick again, but > I am eager to learn] > > If one had a signal of 1v and noise with a peak level of +/- 0.1v then > the output would range between 0.9V and 1.1V. If the signal became 1.05 > V the output would range between 0.95 and 1.15. If we were dealing with > a large number of samples for each signal one could presumably infer > the existence of the change in the signals and even calculate the two > signals by averaging in each case. We could identify the two outputs as > two distinct signals with specified noise. This seems like the sort of > thing people do in statistics. > > It therefore follows (?) that it is possible in principle to > distinguish in an analog system between two signals whose amplitude > varies by less than the noise floor. [I don't think you can do that > with an equivalent digital system with quantisation noise equivalent to > the analog noise floor.] > I appreciate that this only works with a sufficiently large number of > identical signals, and suspect that i am going to be told that it is > irrelevant in an audio context.
Just to recap - quantization noise is an error in the lowest 1/2 bit (remember it's a "rounding error")and so is very tiny in a 16-bit scenario where the signal level of the recording is at minimum -40 to -50dB. You still seem to be searching for something that isn't to be found - i.e. some kind of proof that in 16-bit audio there are tiny variations in level that cannot be captured. The fact is such variations are VERY tiny and would always be swamped by variations in the real noise floor of the recording and replay system, never mind any ACTUAL music that might be playing. Remember that one sample contains data representing all sounds simultaneously occurring - it's the cumulative total of all contributory sine/cosine waves. Since dither is introduced during the recording/mastering process to effectively hide the quantization noise, the whole point is moot anyway :-) If you want to hear quantization noise, record a sine wave in 16-bit at -90dB and play it back with a LOT of gain and no dither. Digital audio (done properly) simply doesn't have the intrinsic "flaw" that too many folks interpret from looking at all of those nasty little staircase sine waves dotted around the Internet. Now, if you are in the habit of listening to -90dB sine waves on their own (you sure won't hear them alongside ANYTHING else!) , I urge you to upgrade to a 20+bit recording/replay chain :-) -- Phil Leigh You want to see the signal path BEFORE it gets onto a CD/vinyl...it ain't what you'd call minimal... Touch(wired/XP) - TACT 2.2X (Linear PSU) + Good Vibrations S/W - MF Triplethreat(Audiocom full mods) - Linn 5103 - Aktiv 5.1 system (6x LK140's, ESPEK/TRIKAN/KATAN/SEIZMIK 10.5), Pekin Tuner, Townsend Supertweeters, Blue Jeans Digital,Kimber Speaker & Chord Interconnect cables Kitchen Boom, Outdoors: SB Radio, Harmony One remote for everything. ------------------------------------------------------------------------ Phil Leigh's Profile: http://forums.slimdevices.com/member.php?userid=85 View this thread: http://forums.slimdevices.com/showthread.php?t=82050 _______________________________________________ audiophiles mailing list [email protected] http://lists.slimdevices.com/mailman/listinfo/audiophiles
