## Digital Data

In a CD (and any other digital recording technology), the goal is to create a recording with very **high fidelity** (very high similarity between the original signal and the reproduced signal) and **perfect reproduction** (the recording sounds the same every single time you play it no matter how many times you play it).

To accomplish these two goals, digital recording converts the analog wave into a stream of numbers and records the numbers instead of the wave. The conversion is done by a device called an **analog-to-digital converter** (ADC). To play back the music, the stream of numbers is converted back to an analog wave by a **digital-to-analog converter** (DAC). The analog wave produced by the DAC is amplified and fed to the speakers to produce the sound.

The analog wave produced by the DAC will be the same every time, as long as the numbers are not corrupted. The analog wave produced by the DAC will also be very similar to the original analog wave if the analog-to-digital converter sampled at a high rate and produced accurate numbers.

You can understand why CDs have such high fidelity if you understand the analog-to-digital conversion process better. Let's say you have a sound wave, and you wish to sample it with an ADC. Here is a typical wave (assume here that each tick on the horizontal axis represents one-thousandth of a second):

When you sample the wave with an analog-to-digital converter, you have control over two variables:

- The
**sampling rate**- Controls how many samples are taken per second - The
**sampling precision**- Controls how many different gradations (quantization levels) are possible when taking the sample

In the following figure, let's assume that the sampling rate is 1,000 per second and the precision is 10:

The green rectangles represent samples. Every one-thousandth of a second, the ADC looks at the wave and picks the closest number between 0 and 9. The number chosen is shown along the bottom of the figure. These numbers are a digital representation of the original wave. When the DAC recreates the wave from these numbers, you get the blue line shown in the following figure:

You can see that the blue line lost quite a bit of the detail originally found in the red line, and that means the fidelity of the reproduced wave is not very good. This is the **sampling error**. You reduce sampling error by increasing both the sampling rate and the precision. In the following figure, both the rate and the precision have been improved by a factor of 2 (20 gradations at a rate of 2,000 samples per second):

In the following figure, the rate and the precision have been doubled again (40 gradations at 4,000 samples per second):

You can see that as the rate and precision increase, the fidelity (the similarity between the original wave and the DAC's output) improves. In the case of CD sound, fidelity is an important goal, so the sampling rate is 44,100 samples per second and the number of gradations is 65,536. At this level, the output of the DAC so closely matches the original waveform that the sound is essentially "perfect" to most human ears.

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