# Dithering

Discussion in 'Mastering' started by blueinkpen, Jul 13, 2004.

1. ### blueinkpenGuest

Hi,

I am curious about dithering. Now, I'm coming from a programming stand-point on this. Here's my thoughts:

In 24-bit sound, the amplitude of the wave ranges from -2^23 to 2^23 units (not decibels, but numeric values). In 16-bit sound, the amplitude ranges from -2^15 to 2^15.

2^23 = 8,388,608
2^15 = 32,768

So to convert 24-bit sound to 16-bit sound, all one needs to do is multiply the value of each 24-bit sample by 32,768 / 8,388608 and put that new value in a 16-bit buffer.

When track volumes are adjusted the program does the same thing. It just figures out what the ratio to multiply by is (according to the slider) and multiplies each sample by that.

So why is dithering used when coverting from 24-bit mixes to 16-bit?

If, for example, someone recorded and mixed all in 16-bit, they would still have the artifacts that come from math error in multiplying by fractions. Why don't they use dithering to mask it?

Maybe I'm missing something and I should stop rambling.
Could someone shed some light on this for me?

Thanks.

2. ### Kurt FosterDistinguished Member

Joined:
Jul 2, 2002
Location:
77 Sunset Lane.
Dither is used to step down from 48 or 96 K to 44.1. If You are already at 24/44.1 dither is not necessary.

3. ### Michael FossenkemperDistinguished past mastering moderatorDistinguished Member

Joined:
Sep 12, 2002
Location:
NYC New York
Wrong!!!

Dither is used anytime a wordlength is changed. Anytime a calculation is done to a word (processing) a much larger wordlength is generated. most daws operate at much higher bit rates (wordlengths) than 16 bit to handle these calcutations with greater precision. if you process a 16 bit word without dither, the calculation errors reside in the 96db range which we can hear. Dither is random noise that is added to the signal to make it more linear and move fraction calculations to the nearest quantize bit. otherwise these great wordlengths are truncated and resolution is lost. do multiple calculations and you end up with tons of information lost. most generic daws truncate to 24 bits which is 144db down and pretty un noticable until you start doing a lot of calculations then it becomes noticable. Most high end mastering gear operates at 40-48 bits and dithers down to 24 bits resulting in greater linearity and resolution. Basically an easy way to look at it is a random rounding formula. Otherwise all the fractions of whole numbers get thrown away. dither randomly rounds these fractions up or down to the nearest bit. Anytime you do anything to a audio file, if you don't dither, your loosing info even if your operating at 24bit and especially at 16 bit.

4. ### Kurt FosterDistinguished Member

Joined:
Jul 2, 2002
Location:
77 Sunset Lane.
I guess Michael told me! That's what I love about RO ... anyone who is open minded can learn new things everyday ... I always belived that word length could be reduced by simply dropping the LSBs (when the math allowed without a remainder) ... Obviously I was wrong ... Thanks for correcting my mistake Michael ..

5. ### AmmitsboelGuest

Kurt, does that mean that you have done productions where you have truncated the signal without dither?
If you use analog tape machines then you don't need dither because the machine makes the noise signal.

I guess that's why it was hot some time ago to ad random noise to the DAW at the time where dither wasn't invented?
Michael do you know the history behind how it started with dither/noise?

Best Regards

Michael
Are those 802's in your studio pics. I bought B&W but wasn't sure if they were good for studio applications. I really like them though. How do you like yours?

7. ### Michael FossenkemperDistinguished past mastering moderatorDistinguished Member

Joined:
Sep 12, 2002
Location:
NYC New York
Yes, they are the N802's and I really like them. There are a select few audiophile monitors that are good for studio applications. These are one of them and are very popular. Dunlavy, Duntech, Egglestons, Wilson's to name a few. Which ones do you have?

8. ### Kurt FosterDistinguished Member

Joined:
Jul 2, 2002
Location:
77 Sunset Lane.
Ammitsboel,
No ... first I don't do mastering. Second my DAW has dither as does my CDR burner. Actually my CDR burner (a Fostex) will automaticly apply dither when needed ... I guess I have been lucky that it does that, after hearing what Michael had to say.

Maybe this could help a bit. There is a great article on Bob Katz's website about dithering. Here is the link to it:

Joined:
Sep 12, 2002
Location:
NYC New York