cliveb;579311 Wrote: > Excuse me for coming in a bit late but I wanted to comment on this. > > "Resolution" and "precision" are two sides of the same coin. Here's an > analogy. Take a 12" ruler - what is the smallest sized object you can > confidently measure the size of? That's the resolution of your 12" > ruler. Now measure something that's about 6" long - what's the accuracy > with which you can measure its exact length? That's the precision. Can > you see that both are constrained by the physical characteristics of > the ruler itself, and are fundamentally the same thing? If you use a > micrometer instead, you'll be able to both measure smaller objects > (better resolution) and more accurately the size of relatively large > objects (better precision). We can liken the 12" ruler to 8 bit digital > audio and the micrometer to 16 bit audio. > > When it comes to audio, both resolution and precision are limited by > the same thing: bit-depth (digital) or noise floor (analogue). They are > just different ways of inaccurately measuring the voltage of a music > signal. > > In particular, analogue does not have unlimited precision, because > although (unlike digital) the voltage it delivers can be any arbitrary > value, the noise floor means that the actual voltage is only an > approximation. If the voltage should be 1V, an anlogue system might > deliver anywhere between 0.999V or 1.001V, and you have no way of > knowing what it should really be. It's a bit like you using that 12" > ruler to measure an object is exactly 6" long - due to its lack of > precision you are only in a position to say that it's somewhere between > 5.95" and 6.05" 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. -- adamdea ------------------------------------------------------------------------ adamdea's Profile: http://forums.slimdevices.com/member.php?userid=37603 View this thread: http://forums.slimdevices.com/showthread.php?t=82050 _______________________________________________ audiophiles mailing list [email protected] http://lists.slimdevices.com/mailman/listinfo/audiophiles
