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XO Wave: A Bit about DitherXO Wave Users: If you are using XO Wave for mastering CDs or creating podcasts, you probably won't need to know any of this because XO Wave's default dither settings are appropriate for 16-bit audio. If you are using high-end hardware, or producing anything other than 8-bit, 16-bit and QuickTime files, please read this page or just skip to the Rules of Thumb for XO Wave Users below, to "cut to the chase". Dither is a complex subject, and although you won't become an expert just by reading this page, hopefully you can learn everything you need to know to use dither well and make great recordings. This introduction tries to use math as little as possible. For more detail, you might want to check out these links:
Analog DistortionDistortion in analog equipment, such as filters, tape recorders, and mixers, is usually harmonic distortion. This type of distortion occurs in many places around us, including our ears and even the air, so we generally do not notice small amounts of harmonic distortion. Harmonic distortion produces sounds that are perceived to be "in tune" with the original audio, meaning that harmonic distortion can be very hard to hear because the added sounds blend in smoothly with the original sounds. Some would argue that in small amounts harmonic distortion sounds good, since it adds a slight color and richness to the sound. In the extreme, of course, harmonic distortion can sound harsh and unnatural, but at low levels and when properly used, it is rarely bothersome. Digital DistortionIn digital equipment, distortion is very different. As long as the resolution is maintained at a high enough level, it is possible reduce distortion to the point where for all practical purposes there isn't any. Audio resolution is usually described in terms of the number of digital bits used to represent each sample. XO Wave, for example, uses at least 32 or 64 bits (depending on your choice of audio engines) to represent samples internally. Audio CDs, on the other hand, only use 16 bits per sample. (Of course, this begs the question: why do we need 64 bits of resolution in XO Wave when we are just making 16-bit CDs? We'll see the answer to this below.) Unfortunately, at some point, such as when burning a CD or sending files over the Internet, we usually need to reduce the resolution of the audio, either because the medium does not support a higher resolution or because we want the files to transfer in a reasonable time, and not take up too much space on disk. When we reduce the resolution of an audio signal, we inevitably throw away some detail. The reduction is normally done by rounding off the less significant data; the lost information is called round-off error, and even though we've actually removed information from the audio, it sounds like we've added noise. When the signal is loud, this is not a problem because the error is small and independent of the signal, but when the signal is small, the error is correlated with the signal in a way that sounds unnatural. Because this inharmonic distortion is not always well-managed on digital equipment, some people describe digital audio as cold and sterile. The SolutionReducing the resolution of digital audio signals results in round-off noise that is correlated with the signal in a bad way. If we were to listen to this noise alone it would sound like a distant, dissonant relative of the original. The relationship between the noise and the original signal is not considered "consonant" or "musical" and so, even at low levels, it can be audible and unpleasant. We cannot eliminate the round-off noise and still reduce the resolution of the audio, but it is possible to de-correlate it from the original source audio. To do this, we add just enough noise to disrupt the relationship between the original signal and the round-off error. When used correctly, this noise, called dither, de-correlates the round-off error from the source audio. The important thing is to use dither before reducing the resolution, because once resolution is reduced, it's too late for dither to help. Some have misunderstood dither as "covering up" the negative effects of round-off error, but that's not quite right. Dither, when carefully applied, actually eliminates the problem: instead of having noise that sounds like an awful version of our original signal, we have noise that sounds like our dither, which is usually much more pleasant. What's more...Very quiet sounds may not be represented at all in your final, low resolution audio, and are therefore lost, the same way that numbers between 0 and .5 are "lost" when rounded. With dither, however, the quiet sounds can be combined with dither 'sounds', to keep them audible. This means that dither actually increases the dynamic range of your audio, so well-done dither can retain detail in the signal that would otherwise be lost. Some people simply do not believe this: after all, it seems like a contradiction to add noise to a signal and actually improve its dynamic range, but it's true. To demonstrate this, here are two 8-bit audio clips of a song with a linear fade-out. They were both produced from the same source, but the second one has been correctly dithered, and as a result the song is audible longer and the fade is smoother: Fade-out without dither: 8-bit WAV file. Fade-out with dither: 8-bit WAV file. The first example sounds fine when the signal is strong, but by the end of the fade-out, the audio starts sounding "chunky" and it pops in and out. The second example, which has been dithered, has a smoother and more even fade-out. Still don't believe it? Try it yourself by exporting your XO Wave session as an 8-bit file with and without dither. (Another common method of demonstrating this is to play a sine wave fading out. It disappears abruptly without dither, but if you use dither it keeps on going and you can actually use a stop-watch to measure the difference. Try it!) Why Use High Resolution?You might be wondering, then, why XO Wave uses such high resolution if we are just going to lose it all when we create 16-bit output files. The reason is that digital audio processing consists of performing a large number of arithmetical operations on each sample. Sometimes hundreds or even thousands of operations are performed on a given sample. If we use low resolution for processing, we are forced to round off our numbers repeatedly, adding noise each time. By working with higher precision (32 bits), we can avoid most of this quality loss. By using even higher precision (64 bits, available in XO Wave Pro), it is possible to reduce the quality loss even further. A simplified example illustrates the problem. Imagine we have a sequence of numbers that represents our audio: { 0, 15, 36, 40, 12, -7, -23 ... }. Now let's say we want to increase the volume by 10% (about .8 dB). To do this, we multiply each number in our series by 1.1, and get this: { 0, 16.5, 39.6, 44, 13.2, -7.7, -25.3 ... }. Looks fine, right? The problem is that if we are representing our audio with 16-bit integers (by far the most common 16-bit representation of audio), we can't represent those numbers and we are forced to round off, so we are left with this: { 0, 17, 40, 44, 13, -8, -25 }. While this example is somewhat contrived, it represents a very real type of problem which crops up in audio processing. The sad truth is that many audio editing packages suffer from exactly the problem just described. For example, some packages offer a "normalize" function which takes in a 16-bit file, multiplies each sample by a non-integer value, and produces a 16-bit file result. Similar methods are used in major commercial packages for everything from creating cross-fades to applying effects. The error from one such operation is generally fairly small, but the accumulated errors from multiple operations can significantly degrade the quality of your audio produced this way. If XO Wave used a low resolution internally, it would have to round off and lose data after each and every operation. The round-off error would accumulate until the audio signal was lost in a sea of noise and inharmonic distortion. The distortion can be avoided by adding dither before each round-off, but we would still be left with the noise, and we might want to perform hundreds or even thousands of operations, without losing the signal. When Should I Use Dither?If you are using XO Wave, you can skip to the next section to find out more about using dither in XO Wave. If you are using another piece of software or hardware for audio processing, here are some tips. Use dither when...
Don't use dither when...
Rules of Thumb for XO Wave UsersHere are some simple tips for using dither in XO Wave. If you want the nitty-gritty on how dithering is performed in XO Wave, see our technical note on Dithering in XO Wave.
-- Bjorn Roche
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