Double Your Bits, Double Your Fun

Mar 1, 2003 12:00 PM, BY OLIVER MASCIAROTTE

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If you own a digital desk, either in hardware or software, then you routinely throw away from two to eight bits of your hard-earned 24. As I asked last month, should you care? Not really, because you can't do anything about it. But you can work smarter within the constraints imposed by necessity. This time around, we're gonna take a look at one of the most basic questions a budding audio novice asks: “Mommy, why do we need 24 bits when our hearing's only 20?”

Let's start with young Elizabeth's question. Her mom has told her time and again that her hearing has a range of about 120 decibels from the quietest perceptible sound to the “threshold of pain,” the loudest sound pressure tolerable before instantaneous hearing damage occurs. Even though — when considering our hearing's dynamic range — we are talking about sound-pressure level, we can still use the same ratio measuring system — the decibel or dB — to measure the dynamic range represented by AES data. Twenty bits' worth of dynamic range is about 120 dB, as each PCM bit represents about 6 dB of amplitude. So, young Liz has nailed the number, and to answer her question, we need to look at gain staging: juggling gain through a complex system to maximize resulting dynamic range and minimize accumulated noise.

Okay, think about this: Take two signals — acoustic, analog or digital — and add them together. The resulting mix is usually louder, though there are exceptions. Take that concept and apply it not only to mixing, but EQ'ing and processing, and you can see that, without a bit of forethought on the part of a system designer or engineer, the final gain will either not take advantage of the dynamic range available in the system or will quickly overload some bus. Too little or too much, neither is good, and usually the problem leans toward too much signal and not enough dynamic range in which to fit it.

So, how does a designer deal with this dilemma? Well, remember earlier when I said that a PCM bit encodes about 6 dB of dynamic range? Looking at that from another angle, you can think of dynamic range as being expressed as word length: A word length of 16 bits encodes roughly 16 times 6 dB, or 96 dB of dynamic range; and a 20-bit word encodes about 120 dB. The AES/EBU protocol can carry a 24-bit essence, enough for a solid 20 bits of signal (thank you, young Elizabeth), plus four additional low-level bits generated by processing.

Now that we're past the basics, let's look at one of the most overlooked features of better-quality digital audio geegaws and the whole point of this month's column. A bonus for the discriminating buyer and a boon to those who value retention of low-amplitude detail, double-precision calculations are one of the keys to better bits. Double-precision is akin to the American Way: If some is good, more is better. Most products use single- precision arithmetic, though, if you dig a bit (yuk yuk), you find a few pearls in among the swine. Double-precision fixed-point would employ two times 24, or a 48-bit word length; double-precision floating-point would use a two times 32, or 64-bit mantissa. Twice as many bits allows low-amplitude details to be retained rather than lost to rounding or truncation. Low-amplitude signal retention is one area where a DSP programmer distinguishes him or herself, as I feel this is a key differentiation between truly professional products.

GAIN STAGING FOR DIGITAL MIXERS

NUMBER OF CHANNELS TO MIX

GAIN REDUCTION IN DB PER CHANNEL

3

4

2

8

3

4

16

4

8

24

5

8

32

5

8

48

6

16

64

6

16

80

7

16

112

7

32

144

8

32

176

8

32

240

8

64

304

9

64

So, how do twice as many bits help retain subtle details in your material? Here's an example: Take two numbers, representing the instantaneous amplitude of signal and some amount of gain change being applied to that signal:

0.92 [original signal amplitude] × 0.707 [negative gain] = 0.65044 [resultant signal amplitude after gain change].

Notice that the result of multiplying those numbers produces a new number with many more digits than what we started with. Think of how many gain changes — which includes panning, EQ and mixing — occur during the course of a typical project, and you'll get some idea of how 24-fixed or 32-floating bits can get “filled up” rather quickly. Those low-order bits, say the 22nd through 24th, carry low-amplitude detail in the data.

Another example — basic gain staging in a digital mixer — should drive the point home. When two or more signals are summed or mixed, the result is usually louder than either source. The table below shows a chart of the amount of “padding,” as it was called in the analog days, or negative gain needed vs. the number of channels being mixed in order to prevent overload in the downstream mix bus.

Looking at those numbers, it's plain to see that with 144 channels to mix, a whopping 8 bits of gain reduction must be applied to each input channel prior to mixing. Those eight lower-order bits, the quietest stuff, must be handled in one of four ways: truncated or tossed away, the cheese-ball approach; rounded up or down to the nearest integer, a better method; re-dithered and wordlength-reduced, better still; or stored as double-precision.

Storing the data as double-precision retains most of the low-amplitude detail and postpones the inevitable wordlength reduction until the end of the production cycle. However, understand that there isn't a standard for double-precision data interchange between products, so files and AES/EBU output both end up as single-precision between processing islands in the production chain. Still, a few host-based DAWs, such as Audio- Cube and Sonar XL, have double-precision modes, while SonicStudio HD, a hardware-based DAW, is fully double-precision throughout. The Cakewalk folks at Twelve Tone Systems advertise Sonar XL as having “all of the capabilities of Sonar, plus two 64-bit, fully automatable DirectX 8 mastering effects.” Notice the mention of “64-bit,” which indicates that the plug-ins are double-precision floating-point. My guess is that more gear will join this elite list as vendors attempt to differentiate their offerings based on quality rather than price.

I hope that this month's rant hasn't caused your head to rotate at too high a speed and has helped you to understand why some gear sounds like crap at any setting except 11. Hopefully, it will also aid you in making more informed decisions when you need to choose or expand your technology base in days to come.


This column was written while under the influence of the original quadraphonic version of Mike Oldfield's Tubular Bells. For a downloadable spreadsheet of the table, along with lots of hand-tooled links and useful information, head on over to www.seneschal.net.

Need help gain-staging in your digital mixer? Download this handy chart. (Excel format)






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