What is meant by 0dB?

I have seen the term "0 dB" used on here quite a bit, but I'm really struggling to understand it.

I generated a screenshot from Audacity to illustrate my dilemma.



The software provides an option to "normalise" the volume to the maximum a CD can accomodate. As I understand it, that value is 0dB.

But, isn't dB a measurement of sound amplitude (or whatever)? The LARGER the number of dB, the louder something is at a given distance.

120 dB is bad for the ears, but 0 dB sounds a little tame!

TIA,
Stephen

 

Hi Stephen,

Decibel (or dB) is a term used to describe relative loudness.
To make it more confusing, the term is used in several different ways.

A few examples (far from a complete list):

db SPL is used to describe sound pressure level or perceived loudness. When you refer to 120 dB being "bad for the ears", you are talking about 120 dB SPL.

db FS refers to decibels related to full scale, which is what your Audacity program is talking about. Digitally stored information is represented with 1s and 0s. A "16 bit word" as is used for CDs, would look something like "1001001101110010". That would represent an intermediate level. Silence would be "0000000000000000" and the absolute loudest signal that can be stored (0 dB FS) would be "1111111111111111".
(For more on digital levels, see "Declaring an end to the loudness wars" at:
http://www.barrydiamentaudio.com/loudness.htm )

With digital recording, we tend to count down from 0 (the top). In other words, a sound that is 6 dB quieter than the maximum would be refered to as having a level of -6 dB FS (i.e. 6 dB below full scale).

So 0 dB FS (the loudest digital level) is not at all the same thing as 0 dB SPL (the quietest "live" level).
There are several other dB measurements for different applications, such as dBv or dB VU.

Hope this helps.
Barry
www.soundkeeperrecordings.com
www.barrydiamentaudio.com

 

No. Since audio signals are bipolar, and to make signal manipulation easier, digital audio uses signed PCM, and specifically the two's complement form of binary numbers. For 16-bit PCM, you have a range of sample values that vary from -32768 to +32767, which in two's complement is represented by the range 1000000000000000 to 0111111111111111, with 0000000000000000 equal to the zero value. 1111111111111111 equals the smallest negative step (sample value = -1), and is the cause for a distortion mechanism in conventional PCM converters because as the signal changes from -1 to 0 all the bits toggle.

 

Hi Black Elk,

Good point. I forgot the twos complement.
By what binary number is the maximum possible level represented?
Are you saying the high order bit would be a zero?

Best regards,
Barry
www.soundkeeperrecordings.com
www.barrydiamentaudio.com

 

Hi Barry,

Not to speak for Black Elk, but yes. The high order bit would be zero. 01111111 11111111 would represent 32767, while 1000000 00000000 would represent -32768 (spaces present only for clarity). I don't know how this specifically works in PCM storage, I'm just familiar with binary representation.

 

Hi Andrew,

Thanks for the clarification.
Yeah, I forgot the twos complement.

And thanks Black Elk too.

Barry
www.soundkeeperrecordings.com
www.barrydiamentaudio.com

 

You caught me mid correction, too. I had initially written 11111111 11111111 as -32768, while it is actually 10000000 00000000.

 

When referring to power, the dB value is:
10 * log (P1 / P0)

When referring to amplitude, the dB value is:
20 * log (A1 / A0)

P0 and A0 are the reference power and amplitude in the ratios. In sound pressure level (SPL) the reference is 20 micropascals, the threshold of human hearing.

-3 dB is approximately half the power.

For more reading:
http://en.wikipedia.org/wiki/Decibel

 

1111_1111_1111_1111 in 16-bit 2's complement binary is -1 in the base 10 (decimal) system. To find the inverse of a binary number in the 2's complement system, just invert all bits and add 1. There is one more negative number than positive.

 

I know. I had just initially written it as -32768. That's why I corrected it, and hid under the chair in embarassment at Barry quoting me first.

 

Andrew,

Here is your chance to climb out from under the chair. What does 1111_1111_1111_1111 represent in a 16-bit 1's complement system?

 

-0

 

Right answer. Wrong answerer.

 

Has anyone noticed that the question in the thread title has not been answered explicitly, yet?

 

Actually, 0dB on its own means very little. As has been pointed out in other reply posts, it is merely a reference level and usually denotes the maximum or optimum level. It's more accurately denoted with a letter after it such as as 'r' or 'm' or 'u', which denotes a unit of reference. In the case of sound pressure, the reference is 0dB spl. This actually denotes an inaudible energy level to a normal ear and hence any level above 0 is audible. 120dB spl is considered to be the highest level that can be tollerated and is also often referred to as the threshold of pain. This is how the magic 120dB figure for the dynamic range of the human ear came about.

So there it is. If you are still confused then don't worry too much because you're in good company.

 

Thanks to everyone for replying. I temporarily lost my post - as it was moved to here from the Music Corner forum.

I'm still a bit confused, as the screen shot within audacity (above) has a scale up the left hand side going from 0.0 -> 0.5 -> 1.0. What does that refer to?

TIA,
Stephen

 

0.0 = silence
0.5 = half the 16-bit scale (value of + or -16384 or -6db)
1.0 = full scale or 0db

Or so I would assume.

 

That refers to normalized linear amplitude. In any system, a bipolar signal can swing between -V and +V volts, where the value of V is usually chosen to comply with certain standards for interfacing consumer and/or professional audio components. However, the characteristics of the audio signal are not defined by the absolute signal level, but by relative level. Therefore, you can remove the value V, and make the signal swing between -1 and +1. In metering the signal, one doesn't care if the swing is positive or negative, and so when the amplitude reaches -1 or +1 you have a full-strength signal, and that corresponds to the 0 dB level. A signal of amplitude -0.5/+0.5 would equate to -6 dB, while a signal of -0.1/+0.1 would be -20 dB relative to the maximum, and so on.