XO Wave: A Bit about Dither

XO 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:

• Nika Aldrich wrote a very good description of dither here. Aldrich spends some time with oscilloscopes and waveforms to show how dither works and explain why it is useful.
• Digital Domain has an excellent page on dither here. This page goes into some detail and is well worth the read.
• To find out how dither is used in XO Wave, see our technical note Dithering in XO Wave. You may also want to see our related technical note Resolution in XO Wave.

Analog Distortion

Distortion 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 Distortion

In 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 Solution

Reducing 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...

• You are reducing the resolution of audio. For example, if you are converting a 16-bit file to an 8-bit file, make sure you are adding dither before the conversion.
• You have finished processing an audio sample and are returning it to its previous resolution. For example, if you are using a program that takes a 16-bit file in, applies an effect, and creates a new 16-bit file with the result, make sure that program dithers properly.

Don't use dither when...

• You are not reducing the resolution and you have not done any processing. For example, if you are creating a 16-bit file by looping another 16-bit file, you probably won't need dither.

Rules of Thumb for XO Wave Users

Here 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.

• File Export: When exporting to a file, you should use dither if it is available; this is the default behavior.
• Playback: In general, you should set the dither in the Hardware Settings window as follows:
  • If you are using 8-bit hardware, or wish to roughly simulate 8-bit output, select "Dither to 8 bits". Note that nowadays 8-bit audio hardware is uncommon.
  • If you are using 16-bit hardware, or wish to roughly simulate 16-bit output, select "Dither to 16 bits".
  • If you are using higher resolution hardware, select "No Dither".
  • If you are using another piece of software such as Audio Hijack Pro or Jack to process audio after it is produced by XO Wave, you should select "No Dither". In this case, you should also make sure that the other software performs proper dithering as needed.
    FYI: Jack's "shaped" dither appears to be most comparable to XO Wave's dither. Audio Hijack Pro can provide dithering through additional plug-ins; XO Audio has not tested this dithering.
  • If your session's sample rate does not match a sample rate provided by your hardware, Mac OS X will automatically perform a sample-rate conversion on XO Wave's output. In this case, the effectiveness of XO Wave's dither may be reduced, especially if the sample rate conversion is extreme. You will have to experiment to see if the output is better or worse with dither. Exported files are not subject to sample-rate conversion by the OS. (Note that ALSA, Jack and OSS may also be configured to perform sample rate conversions, or other processing which reduces or eliminates the usefulness of XO Wave's dither).
  • If you require bit-transparency, select "No Dither". An example of this is if you are editing a 16-bit file without using any effects (including volume), cross-fades, or mixing. However, if you change your mind and decide to add an effect or even just a little volume, you'll want to be sure to use dither.

-- Bjorn Roche