adamdea;578884 Wrote: > ... > > I see that as the sound gets louder the difference between peak and > trough gets wider. I think I understand the illustration about > precision. Is it correct that the error you refer to as a result of > fixed precision is the same as quantisation noise? (ducks). > Yes this is Quantization Error/Quantization Noise and is what happens in an ADC - which is really what we are describing in these examples. A DAC doesn't have this issue because it only plays back EXACTLY the samples given to it - it doesn't have to make tough choices about intermediate values, like an ADC does.
The Quantization Error in an ADC is what is addressed by either: 1) adding dither or noise shaping to "randomize" these erorrs so you can't hear the granularity in very low level signals 2) recording with more bits so the errors are far fewer and lower in level. adamdea;578884 Wrote: > ... > If you reduced by 24 db would you get 8 8 8 9 8 8 8 8 8 7 8 8 8. (I > said 24 db because you said it was a 6 db reduction in your example > but I confess I don't understand the 6 db equivalence. I just mean > getting quieter to the point where the peak becomes 9 and the trough 7) > > > ..and below that level it would just be 8s? > This is a 4-bit example. Each bit value is double the previous bit (8-4-2-1 ... binary math). Doubling in audio = approx 6dB. with 4 bits you can only capture a total of 24dB of dynamic range... So if you reduced the level by 24dB you would have nothing! (silence) Remember the smallest amount you can reduce by is 1 bit... so you just keep taking one bit off both the top and bottom values until you are left with all 8's. So in the 4-bit example, you can reduce a full scale (15-0) wave 7 times/steps until both 15 and 0 become 8. (actually I've just realised in all my examples it is 7 that is the zero-crossing point, not 8 - doh! schoolboy error, I must learn to count). adamdea;578884 Wrote: > ... > Is the point at which it becomes all 8s the resolution of the system > (or is perhaps the other way round- is the point at which a signal > stops being all 8s the resolution?) > > Is there a way of illustrating noise (other than quantisation noise) in > this example > Resolution is number of bits used to capture the signal. It defines the number of different steps in level available from max to min. 4-bit = 16 possible values but remember these come in pairs around the crossing point so really its 8 steps including silence... This in turn defines the QUIETEST sound that can be captured (1 bit above silence) relative to the loudest sound that can be captured. This is the dynamic range! So if you were recording a 100dB real world signal and 100dB was going to be full-scale (15-0), the quietest sound you could capture at the same time would be 76dB. This is why we don't use 4 bits... :-) Recap: the smallest variation in signal that can be captured is 1 bit. The effective audible resolution depends on the number of bits in total, as that defines the difference in level between the loudest and quietest sounds and therefore what each bit is "worth"... Noise (other than QN) is produced in the analogue circuitry of the ADC/DAC. It is very low level. It has nothing to do with bit-depth per se. The reason why 24 bit ADC's and DACS are really 21-bit in practice is that the noise (which is a constant and comes from the thermal or Johnson noise in resistors etc) is greater than the level that can be captured/generated by the sum of the lowest 3 bits. The noise is a constant, but if you record AN ENTIRE TRACK at low level you will have to turn up your amp to hear it... and the noise gets louder too. At a very low level of recording, you will eventually lose the signal in the noise floor... In the 4-bit example, the noise floor is only 24dB away from the loudest signal!. I think perhaps you are trying to look for something that just isn't there? There is no fundamental flaw in the digital process that has not been addressed one way or another. The biggest danger is using too few bits or recording things at too low a level in the first place, such that the signal is too close to the noise floor. 24-bit helps both of those and in practice 16-bit is good enough in many circumstances. The use of 24-bit recording also reduces the need for dithering or noise shaping, since the bottom 3 bits effectively provide that "random noise element" anyway... adamdea;578884 Wrote: > ... > I am also wondering what happens when the 4 bit DA converter now only > has 3 bit resolution > Remember we are talking about ADC, not DAC. A 3-bit ADC would be exactly the same as the 4-bit one except that its max dynamic range would be 18dB. adamdea;578884 Wrote: > ... > In the example you give the crossing point is midway between the > highest and lowest possible values which can be expressed. As you > increase loudness it would "max" out at the same time it "mins" out. > Can you have different triangular waves with the same difference > between peak and trough, but with a different crossing point? > (obviously you can mathematically, but I am wondering whether this > corresponds to a possible sound wave). The only way in which the wave would be aymmetric around the zero-crossing point over a long period of time/number of samples would be if a large DC element existed. This would be a VERY BAD THING. Can you remind me again what exactly it was that you were trying to get to grips with? I think I've lost the thread :-) -- 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
