Digital audio 10
Analogue to digital audio conversion - Word length and quantisation
- Video
- Script
Welcome to this video on digital audio word length and quantisation.
We have learnt how sample rate, the first primary parameter of analogue to digital audio conversion, determines the highest audio frequency that can be recorded without distortion. The second parameter, word length, determines the accuracy of each sample measurement.
In digital audio, each sample is represented by a single byte. Word length determines the number of bits in each byte. Bytes with a longer word length are capable of representing a greater range of values.
For example, a 4-bit byte can represent 16 values, an 8-bit byte 256 values, a 16-bit byte 65,536 values, and a 24-bit byte 16,777,216 values.
Word length | No of possible values |
---|---|
4 | 16 |
8 | 256 |
16 | 65, 536 |
24 | 16,777,216 |
If you have a tape measure that only has centimetre division markings on it, you will only be able to measure to the accuracy of a centimetre. All measurements that do not fall exactly on a centimetre division will have to be rounded up or down. If you require greater accuracy you will need a tape measure with millimetre divisions marked on it. The tape measures in this example are analogous to differing word lengths.
In digital audio, longer word lengths provide a converter with a more accurate "tape measure", or scale, to measure amplitude with, thereby producing more accurate measurements. Better accuracy means the shape of the sound wave is converted with less distortion, which results in a more accurate recording with a lower noise floor.
Word length in digital audio is also sometimes referred to as resolution or bit-depth.
If an analogue to digital converter is set to operate at an 8-bit word length, each sample measurement will be recorded as an 8-bit byte with one of 256 possible values. These values, or divisions, are also known as points of resolution.
A scale with 256 points of resolution is not very accurate. If when a measurement is taken, the amplitude of the wave does not fall exactly on one of these points, then the measurement must be rounded up or down to the nearest point. This process is called quantisation and results in a distorted recording of the true shape of the wave.
A sample measurement which has been rounded up or down is known as a quantisation error and produces quantisation distortion. At loud signal levels quantisation distortion is heard as noise, similar to analogue noise, but at low signal levels it is heard as unwanted audible distortion.
The effects of quantisation errors are most apparent at shorter word lengths. Longer word lengths increase the quality of sound but also the quantity of data and therefore file sizes. 16-bit bytes are of course twice as big as 8-bit bytes. For example, CD quality sound uses a 16-bit word length and requires 5Mb of storage space for 1 mono minute, or 10Mb for a stereo minute. Put simply ..
Shorter word lengths produce ..
bigger quantisation errors
more distortion
.. and ..
smaller file sizes
Longer word lengths produce ..
smaller quantisation errors
less distortion
.. and ..
larger file sizes
One way to quantify the quality of differing audio word lengths is in terms of the dynamic range they allow. As we know, dynamic range in a digital audio file or device is defined as the difference between peak level and the noise floor, and the noise floor is determined by the amount of quantisation. In simple terms, the longer the word length the greater the dynamic range.
The following table shows the dynamic range of the primary word-lengths used today ..
Word length | Dynamic range in decibels (dB) |
---|---|
8 | 48 |
16 | 96 |
24 | 144 |
We can calculate the dynamic range of a digital system by multiplying the word length by 6.
As well as producing more accurate measurements of amplitude, longer word lengths have another advantage. Every time audio is processed during mixing, it can lose some of its resolution. Processes such as EQ, compression and time stretching can degrade the quality a little. It is therefore good practice to use a longer word length during production than that which will be used for duplication and distribution.
It is common place for DAW software to carry out processing at 32-bit or even 64-bit word lengths. This is because calculations for processes such as EQ-ing, compressing and mixing can produce results that require a greater number of decimal places, or longer word lengths.
For example, if we have a signal at 97dB and we reduce it to half it's amplitude, it will be at 48.5dB. In binary it will require more bits to store the result accuraetly.
It is important to understand that using longer word lengths for processing does not elevate the quality of audio, which is still determined by the word length setting of the project, or at the recording phase of a production. However, using longer word lengths ensures that quality is maintained because it prevents bits from being rounded up or down or thrown away.
It is common practice to record, process and mix at 24-bit, before converting files to 16-bit for CD duplication or download. Converting involves a process of down-sampling and dithering during mastering. These are discussed in another of our videos.
The script for this video, with accompanying images, can be found at projectstudiohandbook.com
We suggest you subscribe at our YouTube channel, and join our mailing list at our website to receive notification of new videos, blog posts and subscriber only extras.
Thanks for watching.