Quote:
Originally Posted by GreenLeo /img/forum/go_quote.gif
Can you explain further why a bit is 6dB? I just do not understand what does the 24db record? Is it the loudness of the signal or the voltage of the signal?
Thanks.
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Why 6dB per bit:
In digital audio, you "take samples" of the sound, and then place a value on each sample. You can think of it as placing a transparent grid on a drawing on "going for the closest" point of the grid. The vertical lines of the grid are for sample time, and the horizontal lines are for sample value (sample amplitude).
We will focus on the horizontal lines.
In the real world, each sample is assigned the value of the closest horizontal line just below it.
Think of money. Say one buys an item for one $1.05, but the tax is 3%. That gives you a total of $111.1419048.... As you can see, we go for the closest penny and settle for $111.14
Similarly, we have to settle for some precision in the digital word, and only accommodate "good enough" number of bits". We can just "keep going forever", nor do we need to.
So say you have only 2 bits. That means the horizontal grid is made of only 4 lines. Now add a bit. You now have 3 bits. Adding that bit means adding a new horizontal line right smack at the middle, between the each "existing" lines of the 2 bit system. (With 3 bits you have 8 levels).
Now, add another bit, with 4 bits you have 16 levels. In fact, you take the 3 bits grid, and add a new line between each pair of "existing lines".
So each additional bit DOUBLES the number of quantization levels (horizontal lines). In fact, the space between the lines (quantization error) is halved for each added bit.
With a voltage linear system, twice the voltage, would mean twice the loudness. With a power linear system, twice the power, would mean twice the loudness. But the ear is not at all linear.
Now we want to go with that above information and apply it to the ear. The ear reacts to loudness with a scale that is nearly logarithmic. So what is a factor of 2 mean?
The dB scale for voltage is dB=20*log(X) so we plug in X=2 and get
dB=6.02
In the "logarithmic world", multiplication is turned into addition, division becomes subtraction. So double the number of lines means adding 6dB. Half the error means 6dB more dynamic range. Half the error again means 6+6=12dB... and so on
This all may sound strange. Why is ear logarithmic? For that you have to address mother nature. One way to "reason it" is protection of our hearing. As things get louder, the ear response becomes lesser and lesser... That way we are protected from some huge acoustic power damaging our hearing.
If one is not into the math and engineering, think of loudness being perceived accordion to a "curve" that translates voltage (or power) into loudness in some way that can be figured mathematically or graphically, and it is not a "straight" conversion.
So how many quantization lines do we need? That does depend on the ear, but with 20 bits, that is plenty good, we can not hear better then 20 bits in the most extreme cases!!!
Note that while each additional bit (new horizontal line), you get closer to the sample values, at some point, with enough grid lines, the spacing is so close that there is not much to be gained from more quantization lines. At 20 bits, you have a round 1 million lines! That is 6dB X 20 = 120dB.
So why 24 bits? Well in the computer world, much is being handled in "multiples of 8 bits", which is a byte. As long as we had a 16 bit format, it was 2 bytes. The minute you went for 17 bits, the hardware and software required one more byte, and 2 X 8bits = 24 bits. The last bits are just there, they do not help the music, because the signal never gets to be 24 bit accurate. We can not do it, because of analog noise, and we do not need it because the ear does not hear 144dB.
Regards
Dan Lavry
Lavry Engineering
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