Sample-Rate Conversion is the process of increasing or decreasing the sampling frequency of digital audio.

The sample rate is defined as the number of units, or samples, per unit of time (usually seconds). For instance, a 44.1 kHz file contains 44,100 samples for every second of audio, per channel. An 88.2 kHz file would contain twice as many. Generally, the higher the sample rate, the closer you come to emulating the analog world (continuous in the time domain). Note that increasing the sampling frequency, after recording to a digital medium, will not increase the audio quality, but it can help maintain quality throughout any further digital processing. 

Higher sample rates, while recording, also allow us to capture higher frequencies. We use something called the Nyquist Theorem to determine that the highest frequency (in Hz) that we can capture is equal to half of the sample rate. 

Nyquist Frequency = the highest recorded (or sampled) frequency in Hz = ½ Sample Rate

The most common use of Sample Rate Conversion occurs when preparing a mastered audio file for distribution. In most cases, it must be at a final sample rate of 44.1 kHz for CD.

Referring to the Nyquist Theorem, we can think about why 44.1 kHz is the standard. ½ of 44,100 Hz equals 22,050 Hz. This is generally the frequency limit of human hearing, if not a little higher.

In order to change the sample rate, or frequency, in either direction, an algorithm analyzes the audio and computes new samples at the desired resultant frequency. The quality of the result is determined by the quality of the conversion algorithm and all are not created equal.

The second conversion option is to convert the digital signal to analog and record it at the desired sample rate. The quality of this process is completely dependent on the quality of your D/A and A/D converters.

For a side-by-side, visual, comparison of the different sample rate conversion algorithms, head over to iZotope and Apple's conversion algorithms (used in Audiofile applications) are both represented.

Here are some additional resources regarding this process: