Word-length
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Digital word-length
*Although much literature uses the term 'bit-depth' rather then 'word-length', we chose the term 'word-length' simply because we feel it better describes the mathematical aspect, as well as help to visualize the implication of the technology. It is no more correct or incorrect then using 'bit-depth'; the two terms are synonymous.
Introduction
Word-length (also known as bit-depth) indicates how many digits are used to represent a value in a digital word. For instance, a word-length of 8-bits (8 digits) can only have values from 00000000 to 11111111 (in decimal, 0 to 255). A word-length of 16-bits can have values from 0000000000000000 to 1111111111111111 (0 to 65,536). A digital word doubles in resolution with each bit. For example a 16-bit sample has twice as many possible values (65,536) as a 15-bit word (32,768).
A hypothetical situation to help understand the limitations of word-length
Since each bit (digit) doubles the number of ways to describe the value of something, an example is given to show how a limited set of descriptors (bits) can limit the accuracy (resolution) of your description.
Imagine having to describe to someone the color of a specific car in a parking lot. Imagine the car is 'emerald green'. Imagine this parking lot has 1000 cars in it, and every car is a different color (all the colors are equally spaced along the color spectrum).
Now, imagine you had a list of only 8 colors you could choose from to describe the color of this car (for example: white, yellow, orange, red, blue, black, green, purple). When you say 'green', it is likely that your description applies to 125 cars of various shades of 'green' that are in the parking lot (8 color descriptions results in 12.5% error).
Now imagine you were able to add a light/dark qualifier to the color (for example, 'dark green' or 'light green'). With the darkness qualifier, the number of total possible descriptors doubles to 16, and your description would now only apply to 63 of the cars (16 color description combinations results in 6.25% error).
Now imagine you were able to choose from a list of 255 named colors (such as 'forrest green' or 'kelly green'). You would be able to narrow your description down to 4 cars (0.392% error). If 'emerald green' is not in the list of 255 colors, it might fall somewhere between 'kelly green' and 'forrest green'. One of these descriptors would have to be used, but it would not be very accurate.
As more descriptors become available, your description can become more accurate. This is also true with digits (or bits) in a digital word. As your digital word increases in bit-depth (or word-length), it also becomes more accurate. A 3-bit word results in 8 possible descriptors (12.5% error). A 4-bit word results in 16 possible descriptors (6.25% error). An 8-bit word results in 255 possible descriptors (0.392% error). As we can see, the more bits we have available in our digital word, the more accurate our digital description becomes.
Word-length in digital audio
The word-length of an audio recording limits the resolution of the sample by effectively limiting how far we can 'zoom-in' on the analog signal when it is digitally sampled.
When an analog audio signal is digitally sampled, the voltage on the analog line is sampled several thousand times per second (determined by the sample-rate). Each sample is a 'snap-shot' of the analog waveform at that given moment in time. The sample is a digital word, the value of which is representative of the amplitude of the analog voltage at that moment. With an increase in word-length, the analog voltage can be measured with a finer resolution, making the sample a more accurate description of the value.
For this reason, as digital audio advances, word-length may be the most critical factor in managing to digitally represent an analog audio wave accurately. The more possible values you have to represent your analog audio, the more accurate your samples become. Certainly, sample-rate is a critical factor as well.
Common digital audio word-lengths
| "Redbook", CD audio | 16-bit |
|---|---|
| Professional audio | 24-bit |
Word-length reduction in digital audio
When digital audio samples are reduced, resolution is inherently lost. Also, if the digital audio is not properly dithered during the reduction, severe distortion will be induced (simply removing the least significant bits without dithering is known as truncation).
For a detailed understanding of why distortion is induced when word-length is reduced without proper dithering, read this article on dither.
*More information on this subject will be added soon. Please check back.
