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All information in these pages is copyright (c) 1989-2003 by Roger Nichols. All rights reserved. Permission for personal reference only, and may not be reproduced by any method without written permission.
A Little of This, A Little of That
by Roger Nichols
This month I am going to try to clear up some points that seem to come up
often. I overheard a conversation in a bar that must have been about digital
recording: “Word. Length does matter.”
More On Dithering
My wife dithers over where to go for summer vacation. “Let’s go
here, or maybe we should go there, or how about just staying home this summer…
maybe, or not.” Dithering is a complex problem. Sitting somewhere on
the fence, you can’t quite polarize your decision to decide one way or
the other. Much like the least significant bit in a 16bit sample.
A bit becomes a “1” or a “0” depending on whether or not
the input signal crosses a threshold. For argument sake let’s say that
the each bit is worth one volt and the threshold is exactly 0.5. When the
input signal gets above 0.5 volts, the bit turns on and becomes a “1”.
When the input signal gets below 0.5 volts, the bit turns off and becomes
a “0.” As the signal level increases nothing happens until the level
gets above 1.5 volts at which time the next bit turns on and the first bit
turns off. This works just like counting to 10 in a decimal system. When you
get past 9, the ones column turns off and you put a one in the tens column.
9 (nine) becomes 10 (ten). In digital numbering 1 (one) becomes 10 (one-zero).
In our digital example, there is no way to tell accurately what the input
signal is when it is more than 0.5 but less than 1.5. Anywhere in that range,
the bit shows “1.”
Lets add some dither to see if that helps us determine the level of the input
signal. Dither is a signal that is added to the input signal. The dither signal
can be random noise, a triangular waveform, or some complex mathematically
derived waveform. We will add a triangle waveform to our signal that is exactly
0.5 (peak-to-peak voltage). This is half of the value of our “bit.”
This triangular waveform that we are adding to the signal makes our bit keep
flipping from “0” to “1” as the combined signal crosses
the 0.5 threshold. If the level of our input signal was exactly 0.5, and we
counted the ones and zeros for exactly one second we would have 22,050 zeros
and 22,050 ones (at a 44.1kHz sample rate). The average signal level during
that second would be 0.5 which is exactly what our input signal is.
Now we change the input signal level to 0.75. When we count the zeros and
ones for a second we get 33,075 ones and 11,025 zeros. This means that 3/4
of the time the signal registered as a “1” and 1/4 of the time the
signal registered as a “0.” The addition of the dither signal has
increased the accuracy of our digital system without adding additional bits.
Dither signals can be added in the analog domain to increase the signal capture
resolution of the A/D converter, or it can be added digitally to increase
the resolution after a 32bit DSP plug-in or after a level change or addition
of reverb. By the way. When you transfer analog tape to digital, the noise
floor of the analog tape makes the signal self-dithering.
If dithering is done correctly, there are no drawbacks to using dither at
every stage of bit depth change. The dither during addition of reverb signals
should add to the dither from earlier operations. I have seen some devices
that ignore dither information encoded from a previous operation. As always
the best test instrument is your ears. Make sure that what you are doing sounds
good to you. Listen to quiet passages, or the section of the recording before
the count-off or after the ending when signals are low. Listen for fizzing
or buzzing. If the noise sounds smooth, then you are fine.
Noise Shaping
Here is where you have to be careful. Noise shaping is a step up from dithering.
It is pretty easy to come up with a good dithering signal, but it takes a
room full of DSP experts and mathematicians to produce a great noise-shaping
algorithm. Because of the artifacts produced, noise shaping should only be
done once at the end of the stream. Most of the time this means “Mastering.”
If you get in a pinch, you can do it twice, but after that you could start
getting some weird whistles and high frequency hissing that may be worse than
the benefit from noise shaping. Different noise shaping methods have different
effects on the music. Different types of music sound better with different
types of noise shaping. I once did a project where most of the songs went
through one brand of processing, but a couple of songs sounded better through
another process.
Here comes the tough part… explaining noise shaping. These are the basic
fundamentals for noise shaping, but as with any complex methodology, you can
accomplish the task in numerous ways. Apogee does it one way with UV22, and
Sony does it another way with Super Bit Map. Most of the plug-in suppliers
offer some form of noise shaping software, but the underlying principles are
the same.
Oversampling digital filters are the basic premise behind noise shaping. An
oversampling filter adds interpolated samples symmetrically between the existing
samples using mathematical algorithms. If you use a four times oversampling
filter, then three samples are added between each actual sample. The spectrum
of the oversampled signal is exactly the same as the original spectrum. With
me so far?
The quantization noise produced during digital sampling is spread evenly over
the entire audio spectrum. When the four times oversampling filter gets done
with the data, the same noise is spread over a larger frequency which means
that only one fourth of the noise is in the audible region. This is a 6dB
reduction in noise. If we used an eight times oversampling filter, then we
end up with an additional 6dB of noise reduction.
During the oversampling process a longer internal word length is used for
accurate mathematical processing. The results of the math are dithered back
to the desired word length. The remainder is delayed and subtracted from the
next sample. This reduces the noise by an additional 1dB in the audio range,
but adds 1dB of noise at 1/2 the sample frequency. At four times oversampling,
the extra noise is piled up at two times the sample rate where it can be easily
filtered out of the audible spectrum. The final result is a more accurate
representation of the original signal we were trying to record.
Output Word Length Selection
Every processor, DAW, and digital console allows you to select the output
word length and the use of dither. If the destination device is a 16bit CD
recorder, select 16bit with dither turned on. It does no good to select 24
bit as the output resolution if you are recording to a 16bit DAT or CD recorder.
If you are recording to a 24bit device like a Masterlink or 24bit DAT machine
or another DAW set to 24bit, then set the output word length to 24bits and
turn dither on. Remember that the internal word length is 32 bits or higher
and dithering retains some of that resolution in your final output. Put a
little sticky note on your DAT machine that says something like “REMEMBER
TO SET WORD LENGTH.” I have so many sticky notes around I even have one
that says “REMEMBER TO READ STICKY NOTES.”
Not The End, Only The Beginning
This is just a very cursory overview of what goes on during dithering and
noise shaping. There is continuous research and experimentation into this
field and improvements are being made every day. If you want to know more
about the subject check out Ken Pohlmann’s book “Principles of Digital
Audio.” Another more technical source is “Digital Signal Processing,
A practical Approach” by Emmanuel Ifeachor and Barrie Jervis. If both
of these are over your head, try “How To Buy Foreclosed Real Estate For
A Fraction Of Its Value” by Theodore Dallow.