| 2. An Introduction To Sample Rate Conversion |
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When we hear a sound, our ears sense continuous variations in air pressure caused by the motion of surrounding objects. In analog audio electronics, these variations in air pressure are represented by continuous variations in the electrical potential, or voltage, in an electrical circuit (figure 1). However in digital audio, the variations are stored as a sequence of numbers, each corresponding to the air pressure at a single moment in time, rather than as a continuous value. It is an amazing fact, backed up by some impressive mathematics, that a continuous sound wave can be completely represented with any specific accuracy by a finite set of numbers.
Figure 1 - Analog Signal From Sound Pressure Waves
The rate at which samples are taken must be at least twice the highest frequency of the sound to be reproduced, and is called the "sample rate," which is measured in Hertz (Hz). For example, a sample rate of 48,000 Hz (48 kHz) means that 48,000 values are taken each second. In the reverse process, the numbers in a digital audio signal are converted back to a continuous signal by means of "digital-to-analog conversion."
Figure 2 - Analog To Digital Conversion Process
The mathematics underlying digital audio guarantees that a digital audio signal gives an accurate picture of the entire original continuous air pressure wave. Thus there must be a way to compute the value of that wave at any moment in time based purely on the sampled values. Through such computations, it is possible to convert a digital audio signal from one sample rate to another, a process known as "sample rate conversion." As shown in figure 3, computing the new sample rate data is accomplished by evaluating the continuous pressure values represented by the original sample rate data, but at moments corresponding to the new sample rate. While mathematically somewhat complex, such a conversion can be done with any desired accuracy. When properly performed, the computational errors involved in sample rate conversion are much smaller than the dither noise of the original signal, and is thus completely transparent to the listener.
Figure 3 - Sample Rate Conversion
