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From digi´s white papers:
A BIT OF DITHER
There is a dithering stage in most double precision plug-ins
and one final dithering stage at the post master output of the
summing mixer. Dither is noise with very specific properties
added to the signal in order to de-correlate the noise floor
from the original signal so that when length reduction
occurs, the resulting waveform does not contain any
harmonic distortion or noise floor modulation artifacts.
This allows the plug-in and the mixer to perform very
precise calculations while maintaining the low level detail
when handing the signal off to the next process. Within
the Pro Tools TDM mixing environment, when the dithered
mixer is used, dither is added to the 48-bit signal before it
is reduced to 24 bits to be placed back on the TDM bus and
sent to the DACs. Dither is not added on a track by track
basis, as this would produce unwanted accumulated noise.
Dither is only added once at the Master Fader output of the
mix bus so the total system dither noise is 3 dB at -144 dB.
“Not so fast!” you say. “You just added noise to my signal and
truncated my word from 48 bits to 24 bits—I’ve been robbed!”
Well, it’s true that within this system topology, the signal must
be 24-bit in order to pass from DSP to DSP via the TDM bus,
but it’s important to understand that the level of the dither
added to the signal is around -144 dB, which is below the
noise floor of the converters. Consider that our ears can deal
with a dynamic range of around 120 dB (from the threshold
of audibility to the threshold of pain). This gives you an idea
of how low “-144 dB” is in terms of audibility—you’d have to
have your monitor system cranked up to extremely high levels
to even hear any sound that might exist in a noise floor this
low. The same could be said about the loss of the lower 24 bits.
The sample values represented by the lower 24 bits in a 48-bit
word are between -144 dB and -288 dB, so the dither only
affects the signal at -144 dB or lower.
THE PRO TOOLS 48-BIT MIXER PLUG-IN
Just as EQs, dynamics, and reverbs are plug-ins, the Pro Tools
Dithered Mixer is a plug-in as well. It differs from most other
plug-ins in that it can grow to span multiple DSPs and as it
grows, it passes signal from DSP chip to DSP chip at a full
48 bits instead of dithering and truncating back to 24 bits.
It does so by using two 24-bit TDM timeslots per connection.
This enables the mixer to maintain an internal dynamic range
of at least 288 dB from beginning to end.
The extra 24 bits in the system are used to provide channel
faders with additional dynamic range above and below the
original 24-bit word, and it guarantees that the same fidelity
is maintained when adding more inputs to the mix bus. In the
Pro Tools +12 mixer, 9 bits are reserved for levels above 0 dBFS,
providing 54 dB of headroom. This is enough headroom to
allow 128 tracks of full code, correlated audio (imagine sample-
aligned sine wave source files) to be summed with all faders at
+12 without clipping the “input side” of the bus. It also provides
enough bits below the 24-bit word to allow channel faders to
be placed at nearly -90 dB before they stop contributing a full
24 bits to the mix.
Since in the real world, audio signals are almost never exactly
correlated in this way, you can mix a far larger number of
inputs within the Pro Tools mixer without clipping the “input”
side of the mix bus at all. You can clip the “output” side of
the mixer, but that’s what Master Faders are for—they allow
you to trim your final output level to avoid clipping the DAC
or 24-bit digital output when your mixed signals leave the
Pro Tools mix environment. This is analogous to an analog
console mix bus, where you trim the master bus with a master
fader to avoid clipping the output circuitry in the console.
Similar to analog mixers, the Pro Tools mixer is comprised of
individual input channels and a summing stage. At the input
stage, each channel’s 24-bit word is multiplied by 24-bit gain
and pan coefficients to create a 48-bit result. The new 48-bit
word contains the original 24 bits “shifted” lower in the 56-bit
register to allow for headroom and “footroom” below unity
gain, enabling channels to be turned down without losing
precision. Specifically, it’s possible to pull any channel fader
down to -90 dB and its signal still retains 24 bits of precision.
As channel faders are pulled down, there is a loss to the lower
bits of the newly extended 48-bit word which represent signals
down to about -240 dB—but a full 24 bits of precision is main-
tained down to -90 dB.
It’s important to understand that while some lower bits
of the 48-bit word are truncated when reducing individual
channel levels, the quantization (or rounding error) that
occurs when they are lost adds about one millionth of a
dB to the total quantization error. This is determined by
adding the quantization noise from the single precision
quantization to the quantization noise of the double preci-
sion quantization. For example, when the mixer represents
-144 dB, the actual value is more like -143.99999 dB and it
is quantized to -144 dB. The difference is about one millionth
of a dB and is astronomically close to the “ideal” mixer—
one that doesn’t ever lose bits internally.
At the summing stage, Master Faders perform in a similar
way to channel faders in terms of resolution. The final gain
stage is in effect a master fader, which is always present;
and, when the Pro Tools UI displays a Master Fader, the user
is given a “handle” to adjust the range of the final gain stage
output. As a built-in part of the mixer, Master Faders don’t
consume any additional DSP resources, so they are the best
way to adjust the final output of an internal bus or external pair
without losing precision.
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