Sample Rate Conversion

Sample rate conversion is the process of converting a (usually digital) signal from one sampling rate to another, while changing the information carried by the signal as little as possible. When applied to an image, this process is sometimes called image scaling.

Sample rate conversion is needed because different systems use different sampling rates, for engineering, economic, or historical reasons. The physics of sampling merely sets minimum sampling rate (an analog signal can be sampled at any rate above twice the highest frequency contained in the signal, see Nyquist frequency), and so other factors determine the actual rates used. For example, different audio systems use different rates of 44.1, 48, and 96 kHz. As another example, American television, European television, and movies all use different numbers of frames per second. Users would like to transfer source material between these systems. Just replaying the existing data at the new rate will not normally work—it introduces large changes in pitch (for audio) and movement as well (for video), plus it cannot be done in real time. Hence sample rate conversion is required.

Two basic approaches are:

• Convert to analog, then re-sample at the new rate.
• Digital signal processing – compute the values of the new samples from the old samples.

Modern systems almost all use the latter since this method introduces less noise and distortion. Though the calculations needed can be quite complex, they are entirely practical given today’s modern processing power.

A famous example of analog rate conversion was converting the slow-scan TV signals from the Apollo moon missions to the conventional TV rates for the viewers at home. Another historical example, part analog and part digital, is the conversion of movies (shot at 24 frames per second) to television (roughly 50 or 60 fields per second). To convert a 24 frame/sec movie to 60 field/sec television, for example, alternate movie frames are shown 2 and 3 times, respectively. For 50 Hz systems such as PAL each frame is shown twice. Since 50 is not exactly 2×24, the movie will run 50/48 = 4% faster, and the audio pitch will be 4% higher, an effect known as PAL speed-up. This is often accepted for simplicity, but more complex methods are possible that preserve the running time and pitch. Every twelfth frame can be repeated 3 times rather than twice, or digital interpolation (see below) can be used in a video scaler.