Sampling

Sampling is the process of converting analogue signals into binary.
Every second, an analogue waveform is measured tens of thousands of times, and each measurement is given a number. It is very similar to a roll of cinema film; each frame is different, but by running the frames quickly through a projector the illusion of movement is created.
An analogue waveform is measured, or sampled. It is cut into slices, rather like a loaf of bread, and each slice is measured. The samples have flat tops, so they don't follow the curve of the wave accurately. If the slices were thinner, the sampled waveform would be more accurate.
The number of times per second that the sound wave is sampled is called the sampling rate.

Common Sample Rates

8kHz (8000 samples per second)	Telephone (pretty bad quality)
44.1kHz (44,100 samples per second)	CD sample rate
48kHz (48,000 samples per second)	Quality pro audio sample rate
96kHz (96,000 samples per second)	Double CD quality
192kHz (192,000 samples per second)	Currently the best available
384kHz (384,000 samples per second)	The next generation, coming soon…

The choice of sampling rate determines the highest audio frequency that can be recorded. Any frequencies above this must be filtered out, otherwise aliasing will occur.
Aliasing is an effect that happens when there are too few samples taken of the original waveform. The D/A converter does not have enough information to accurately reconstruct the wave, and so it introduces a waveform that was not recorded. The aliased sound decreases in pitch as the original increases.
Aliasing also occurs on film; very often we see wheels on film that appear to stop and move backwards. This is the visual result of a sample rate that is too low.
To ensure that aliasing does not happen, we need to make sure that the sampling rate is at least twice the frequency of the highest audio frequency to be recorded. This is known as the Nyquist criterion.
Therefore, if our sampling rate is 44.1kHz, the highest audio frequency that we can record will be under half that. In this case, the highest frequency would be 20kHz.

The other factor in sampling is how the samples are measured. On a graph you can see that each sample (or "slice") is at a different height. If there were only 16 different heights that each sample could be, the sampled waveform would be quite misleading. The finer the measurements, the more accurate the sampled waveform will be.
As digital audio is in binary, we can see how many level steps can be used.

The dynamic range of a given bit rate can be calculated with …

Dynamic Range (dB) = 20 log₁₀ (2^{Bit Rate - 1})

Bit Rate & Dynamic Range			Use
12 bit	4,096 levels	72 dB	Old Akai samplers (e.g. S900)
16 bit	65,536 levels	96 dB	CD standard
24 bit	16,777,200 levels	144 dB	High quality pro rate

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