About Bits

At the same time that we are increasing our sampling rate, we are also increasing our word-length. The CD playback medium currently uses a 16-bit word length. Meanwhile, 20-bit word-length recording and mastering is beginning to become generally available, and there are rumbles abut 24-bit word-lengths.

This dimension – word length – speaks to the resolution of the recording, to its dynamic range. It is common knowledge that each bit in the word yields 6 dB of dynamic range, so that a 4-bit word has a dynamic range of 24 dB (i.e. 4 x 6), a 16-bit word has a dynamic range of 96 dB (16 x 6), and so on.

With that in mind, a 20-bit word should have a dynamic range of 120 dB and a 24-bit word should have a dynamic range of 144 dB, while the dynamic range of our hearing is, comfortably, 120 dB and, uncomfortably, 140 dB. So, 24-bit words oughtta sound terrific!

Naturally, there’s a problem. If you read their sales literature, the sales weasels flogging 20-bit recording systems usually promise about 108 dB dynamic range, not the theoretical 120 dB. Why is this? Well, we have a problem with the noise floor of the analog electronics. The absolute limit for an electronic noise floor is around -126 dBM (see the Sidebar if you want some explanation of these dB references), due to thermal noise, and in practice it is very difficult to keep noise below about -110 dBM (roughly -108 dBV).

So, when we convert, say, 24 bits to analog signal, we’ve got a problem. Either we lose the Least Significant Bits below that noise floor, or the Most Significant Bits become a little too electrically, er, potent for comfort! For example, if we make 0 dB Full Scale (dBFS) equal to 1 volt for the Most Significant Bit of a 24-bit word, then the Least Significant Bit will have a magnitude of -144 dBV, at least 35 dB into the noise grunge. On the other hand, if we make the Least Significant Bit equal to, say, -108 dBV so that we are at or above the electrical noise floor, then 0 dBFS is going to be 36 dBV, or 63 Volts RMS! Smokin!! You’ll probably want to be a little careful patching these signals . . .

Given these opposing limits of noise and safety, what’s the use of the greater word lengths and bit counts? Well, we hear the increased resolution as a “transparency” in the recordings. We can hear signals way below the noise floor. Phrases like “a veil is lifted” and “spatial cues and reverb trails are clearer” abound among the sales weasels and oot and aboot on the Internet as they all wax poetic about the virtues of 24-bit words for digital audio. See the discussion of dither, below.

More to the point, the greater resolution of 20-bit words allows us to really reduce the effect of the errors and problems that accumulate as a recording project progresses. And as mastering engineer Scott Hull puts it, “We need to have greater resolution than the consumers do, so that we can make sure that what they get is free from problems.”

So, be happy to embrace 20-bit technology and look forward to 24-bit, which should really be enough, once and for all! At the same time, understand that there are problems presented by noise floors and safety considerations in the analog realm, and that no amount ‘o bits is going to change those considerations!

About Dither

The other area that merits some reconsideration is dither. Dither, as you hopefully know, is low level noise added to the analog signal prior to conversion to digital, or noise added in the digital realm while reducing the number of bits. It serves the purpose of retaining low-level signal information that exists below the level of the Least Significant Bit, at the expense of added noise. Roughly, what happens is that the addition of dither noise varies the signal amplitude around the Least Significant Bits. This permits signal elements at amplitudes below the amplitude of the Least Significant Bit to be retained in the signal. The net audible result is that while we hear the dither noise, we also hear the signal itself with additional resolution and clarity. Subjectively speaking, the addition of dither “cleans up” the signal very nicely and the net result, noise included, is far more palatable to listen to than un-dithered signal. Tom Bates, who offered a lotof advice regarding this article, suggested that we try to think of dither as a time-sharing technique, where noise and extra bits of signal share the same digital turf, if you’ll excuse the confused metaphor.

There are several issues regarding dither that have come up in the past few years that are worth your consideration. The first is that while dither is often white noise, several other dithering schemes have evolved that use noise that is not white, but shaped in one of several ways to make them less audible than white noise. Thus we obtain the benefits of dither with less audibility of the dither noise. Sony’s Super Bit Mapping (SBM) is such a technique, as are Lexicon’s Psychoacoustically Optimized Noise System (PONS) and Apogee’s UV-22.

There is, as I write this, a fairly lengthy on-line discussion of the benefits and problems related to such noise-shaped dither (particularly Super Bit Mapping) on the Pro-Audio Internet discussion group. The issue came up as a question about whether to send a 16-bit DAT with Super Bit Mapping to a mastering facility, where subsequent signal processing was bound to happen. About half the guys have said definitely don’t do it – let the mastering house add dither, if needed, at the very last stage. As I did research for this article, it emerged very clearly that this is bad advice! Mastering houses want (need?) you to send them longer word-length (higher bit-rate, i.e. 20 or 24-bit) recordings that are either dithered at those Least Significant Bits or else un-dithered, and permit them to re-dither to the 16-bit word-length release format when they are done with other processing.

This brings up the other confusing point about dither these days – re-dithering. You’re supposed to add dither at the beginning, when you convert from analog to digital, right? And that dither should stay with the recording right through to re-conversion to analog, right? How can you lose noise that you’ve added? Why should you have to add more noise later?

There are a couple of reasons why you might need to add dither after you’ve converted to the digital realm. The first would be that you made your original recording with more bits than you have available for either storage or playback – for instance, you are using 20-bit converters but have a 16-bit workstation. That 20-bit converter added dither, of course, but it was added to the Least Significant Bits of the 20 bits. If you simply transfer the output of the converter to a 16-bit format, the four Least Significant Bits will be ignored and the dub will consist of the 16 Most Significant Bits. This is called “truncation.”

Well, the resulting 16-bit recording has no dither, because the dither was eliminated as part of the four Least Significant Bits. You have lost, and cannot recover, any signal information included in the four Least Significant Bits in the original 20-bit signal. If you re-dither at the 16-bit level, you will be able to retain some signal information down to at least the 18th bit, just as you retain low-level analog information through the use of dither.

This raises an interesting question: is it better to convert directly to 16 bits with dither, or convert to 20 bits and re-dither to 16 bits? And why? Tom Bates suggests that it’s probably better to convert to 20-bit and re-dither to 16-bit, based on the assumption that the 20-bit converter with do a better job of handling amplitudes below the 16th bit than will the 16-bit converter, which ostensibly wasn’t designed with such performance niceties in mind. Naturally, this is also a more expensive route, so ya gotta decide for yerself how much it’s worth to ya.

The other time re-dithering becomes necessary is when you are doing a lot of mixing and/or signal-processing in the digital realm. Digital Signal Processing usually involves 24 or 32-bit word-lengths to permit the accurate realization of complex algorithms that stand in for various signal-processing operations. As a function of these various arithmetical operations, signals after Digital Signal Processing (DSP) have more bits in them than are available at the final output. Also, digital attenuation – you know, turning down the faders on your digital console – will reduce the Least Significant Bits that contain the dither information below the level of the Least Significant Bit of the output, causing truncation.

So, you should re-dither any time you are reducing the number of bits in the word-length of the digital audio signal or doing any DSP that may end up changing the number of bits as a function of the DSP. Whew!