Pulse code modulation
lastmod 2018-08-17created 2014-02-124 edits
Pulse-code modulation (PCM) is a digital representation of an analog signal in which the signal level is sampled at uniform intervals and then quantized into a digital (binary) code. PCM is used in digital telephone systems and is also the standard for digital audio in computers and the CD Red Book. It is also the standard for digital video when using, for example, ITU-R BT.601. However, straight PCM is not used in consumer-level SD video such as DVDs and digital video recorders (because the required bit rate is too high). In general, PCM encoding is often used for serial digital transmission.
Sample Rate & Bit Depth
Sampling and quantization of a signal (red) for 4-bit PCM
Sample Rate is the unit by which time is divided. In the figure above, the red curve is an analog signal representing one oscillation. When this signal goes through PCM conversion, it is represented as a staircase, as shown in the figure. If the Sample Rate increases, the horizontal width of the steps in the staircase graph becomes narrower, which means the digitally stored information gets closer to the red analog curve. Sample Rate is expressed in hz. A CD holds data converted by dividing one second into 44,100 parts, so it is said to have a Sample Rate of 44.1kHz.
Bit Depth is the unit by which sound pressure is divided. Just as the horizontal width of the staircase graph in the figure above narrows as the Sample Rate increases, the vertical height of the steps narrows as the Bit Depth increases. The figure above divides the maximum sound pressure into 16 steps from 0 to 15, which is 2 to the 4th power, i.e., a Bit Depth of 4bit. A CD has a Bit Depth of 16bit, which means the sound pressure is divided into 2 to the 16th power steps.
So the larger the Sample Rate and Bit Depth values, the closer the stored digital information (the staircase graph) gets to the analog curve. (Of course, the data size also increases.) If a source was recorded/mixed at a Sample Rate and Bit Depth higher than the CD standard of 44.1kHz/16bit, the mastering process needs to lower the Sample Rate through an Anti-Aliasing Filter and lower the Bit Depth using Dither.
The human audible frequency range goes up to 20kHz, but the CD Sample Rate became 44.1kHz because of the Nyquist-Shannon theorem and the technical issues of the time when the CD was born. As the figure above shows, a sound oscillation starts at 0, moves in the (+) direction, returns to 0, moves in the (-) direction, and then returns to 0 again; this is defined as 1Cycle. If one second is divided into 20,000 parts, only one data point is assigned per 1Cycle, so when converting a 20kHz oscillation, there is no way to represent how far the oscillation moved in the (+) and (-) directions. Therefore one second must be divided into at least twice that, 40,000 parts, i.e., 40kHz or more, so that two data points are assigned to one 1Cycle of a 20kHz oscillation and the magnitude of the sound in the (+) and (-) directions can each be stored. However, in the late 1970s when the CD was first being developed, digitally converted audio data was fairly large, and reportedly there was no suitable medium to store it. So the development engineers reportedly used video tape as data storage, and because the data was stored with the video tape's frames per second and lines per frame in mind, the Sample Rate was settled at 44.1kHz.