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Today, it is difficult to find music sources which are not digital. The audio signals in CDs and DVDs, mp3 and wave files, and digital cable all encoded digitally. Even some "live" performances utilize digital synthesizers and digital amplification. This section explains what is meant by digital audio and discusses its relationship to analog ("real") audio.
Since sound waves are pressure waves we may express sound as a function of time where f(t) is the value of the air pressure at a fixed point for the time t. In this model, t and f(t) are real numbers and may taken on an infinite number of possible values. In the digital world, variables may have only a finite number of possible values. Each value is represented by an integer of finite range or a floating point (decimal value with finite range and finite number of decimal digits.) Thus the model for sound in the digital world is a function which, for each time t (from among a discrete number of times,) f(t) represents the pressure from a discrete number of values. The precision for the time is rated by a term called the sampling rate while the precision of pressure values is usually expressed as the sample resolution.
The sample rate referrers to the number of pressure values that are recorded each second and thus determines the precision for the time variable. CD quality sound has a sample rate of 44,100 Hz and thus the time increment is 1/44,100, approximately 0.00023 seconds.
| Commonly Encountered Sample Rates | |
|---|---|
| Rate | Use |
| 11,025 Hz | Poor AM Radio Quality/Speech (low-end multimedia) |
| 22,050 Hz | Near FM Radio Quality (high-end multimedia) |
| 32,000 Hz | Better than FM Radio Quality (standard broadcast rate) |
| 44,100 Hz | CD Quality |
| 48,000 Hz | DAT Quality |
| 96,000 Hz | DVD Quality |
Sample resolution (the number of bits per sample) determines how many gradations
of amplitude (corresponding to loudness) can be represented in the digital waveform.
Typical values are 8, 16, 24, and 32 bits which represent respectively 256,
65,536, 16,777,216, and 4,294,967,296 quantization levels for the amplitude
values. The range of amplitudes from the most negative possible sample value
to the most positive is referred to as the dynamic range and
is normally expressed in decibels (dB) relative to the smallest non-zero digital
value (i.e., 1). For example, with 16-bit resolution, the largest positive value
representable is 32,767 and the smallest value representable is -32,768 giving
a total range of 65,536 values or about 96 dB. The dynamic range for human hearing
is about 100 dB.
The process of encoding an analog signal into a digital signal is performed by an analog to digital converter (ADC.) The ADC typically consists of an anti-aliasing (low pass) filter, a sample and hold circuit, and the circuit to convert voltages to digital values.
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