Quote: Originally Posted by adamdea ... 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). unquote You can feel free to ignore the bit in brackets. If it is annoying just move on. [I understand the 6 dB = 1 bit equivalence. But in your example when you reduced the peak and raised by trough by 1 from 14 to 13 you described it as a 6db reduction. (I assumed from that that each iteration represented 6db). I wonder whether the reduction by 1 should have been a 3 dB reduction. I was simply reducing the peak etc by 4 more stages in the example I gave. There seem to be 7 reductions before your signal becomes 7s and 8s. I cant see any way of reducing the a 15, 0 starting pair to get either 8 or 7- I wonder whether this is because the crossing point is the same as the median value (7.5). If so I am now baffled as to how one expresses silence in this 4 bit word.(pehaps you ignore 0, leaving 15 values and a happy median of 8).] Now what was the point? Well I was tryign to work out whether we could clarify the previous discussion by actually drilling down to the numbers. I think that it is very difficult to discuss technical (especially mathematical relationships in everyday english. I have noticed for example that on the news they often trip up when tryign to discuss economic (or econometric) concepts like say the distinction between the stock of public debt, the budget deficit, a change in the budget deficit. As to where this takes us 1.1 You have pointed out that in information theory terms i have been confusing two terms "precision" and "resolution". These seem to correspond with 2 problems a. the quantisation noise cuased by the limited choice of sample values b. the inabilty to produce a sound quieter than the lowest value (apparently over or above the crossing value.) 1.2 It seems that an analog sytem has limited resolution but not limited precision. If we return to your post 33, you described radio 3 as 13 bit. I assume that you meant that it had a snr of 78 dB. I have been making the point at various stages (although apparently without using the correct terminology) that whilst a digital recoding may have 16 bit resolution and 16 bit precision, analogue systems can have 13 bit resolution and unlimited precision. OR have I got this wrong and was the 13 bit radio limited in both resoltuion and precision? 1.3 I am assuming that if a sound gets quieter it not only gets closer to the noise floor but the quantisation noise relative to signal increases. II. My major concern was over the example of the 24 bit DAC which has "only" 17 bit resolution. I think this means it can only resolve a sound 102dB below peak. I am however confused as to what this means about its precision. I understand that the DAC doesn't have to guess at the values it is decoding, but isn't the output the same as if it were reading a 17 bit recording with 7 random numbers on the end . Does this not mean that not only does the noise floor increase but the quantisation noise will increase? -- 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
