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Bit rates and sample rates in music

What are Sample Rates and Bit Rates?

Sample and bits rates together define how much information is gathered and how precisely a digital device
will reproduce an analog sound. The sample rate defines the number of times a computer will analyze the sound and
the bit rate determines how the level of detail of each sampling instance.

SAMPLE RATES

Let’s say you were doing a phone interview trying to determine eating habits for all people in the world.
The number of people you called would determine the sampling rate. If you talked to all 6.6 billion people,
in addition to being exhausted, you’d have sampled everone. In the audio world, there are theoretically,
20,000 people to call since the human ear can hear up to 20,000 cycles per second (20Khz).
However, we actually have to sample at least twice that number in order to guarantee that all sound is captured.
This “double” sampling figure is explained by the Nyquist Theorem.

Presumably the Red Book Standard for CD manufacturing settled upon 44.1 Khz as the format for audio CD’s because the sampling rate was slightly higher than the figure required by the Nyquist Theorem. But why did they choose exactly 44.1 Khz? Information on this is not as easy to come by. Below is an interesting explanation found deep in the website of the Columbia University Computer Sciences Department:

In the early days of digital audio research, the necessary bandwidth of about 1 Mbps per audio channel was difficult to store.  Disk drives had the bandwidth but not the capacity for long recording time, so attention turned to video recorders.
These were adapted to store audio samples by creating a pseudo-video waveform which would convey binary as black and white levels.  The sampling rate of such a system is constrained to relate simply to the field rate and field structure of the television standard used, so that an integer number of samples can be stored on each usable TV line in the field. Such a recording can be made on a monochrome recorder, and these recording are made in two standards, 525 lines at 60 Hz and 625 lines at 50 Hz.  Thus it is possible to find a frequency which is a common multiple of the two and is also suitable for use as a sampling rate.

The allowable sampling rates in a pseudo-video system can be deduced by multiplying the field rate by the number of active lines in a field (blanking lines cannot be used) and again by the number of samples in a line. By careful choice of parameters
it is possible to use either 525/60 or 625/50 video with a sampling rate of 44.1KHz.

In 60 Hz video, there are 35 blanked lines, leaving 490 lines per frame or 245 lines per field,
so the sampling rate is given by : 60 X 245 X 3 = 44.1 KHz

In 50 Hz video, there are 37 lines of blanking, leaving 588 active lines per frame, or 294 per field,
so the same sampling rate is given by: 50 X 294 X3 = 44.1 Khz.

The sampling rate of 44.1 KHz came to be that of the Compact Disc. Even though CD has no video circuitry,
the equipment used to make CD masters is video based and determines the sampling rate.

From John Watkinson, The Art of Digital Audio, 2nd edition,
pg. 104

BIT RATES

While talking to the 6.6 billion people indivdually, you could choose to ask them each one question or a thousand questions.  The more questions you asked, the more accurate each sample (phone call would be). Or think of it this way: Rating something on a scale of 1 to 1000 is a more precise representation than rating it on a scale of 1 to 10.
This is pretty much what a bit rate is. Bit rates, or word lengths as they’re sometimes called, define the precision of the sample. So the bit rate defines the number of permutations of the 0’s and 1’s used to describe each digital word or sample.  The bit rate is calculated exponentially as a power of 2 as follows:

16 bits = 216 = 65,536
24 bits = 224 = 16,777,216

You can see how big a theoretical difference there is between 16 and 24 bits.

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