Sample-rate conversion

Sample-rate conversion, sampling-frequency conversion or resampling is the process of changing the sampling rate or sampling frequency of a discrete signal to obtain a new discrete representation of the underlying continuous signal. Application areas include and audio/visual systems, where different sampling rates may be used for engineering, economic, or historical reasons. For example, Compact Disc Digital Audio and Digital Audio Tape systems use different sampling rates, and American television, European television, and movies all use different frame rates. Sample-rate conversion prevents changes in speed and pitch that would otherwise occur when transferring recorded material between such systems. More specific types of resampling include: upsampling or upscaling; downsampling, downscaling, or decimation; and interpolation. The term multi-rate digital signal processing is sometimes used to refer to systems that incorporate sample-rate conversion. Conceptual approaches to sample-rate conversion include: converting to an analog continuous signal, then re-sampling at the new rate, or calculating the values of the new samples directly from the old samples. The latter approach is more satisfactory, since it introduces less noise and distortion. Two possible implementation methods are as follows: If the ratio of the two sample rates is (or can be approximated by) a fixed rational number L/M: generate an intermediate signal by inserting L − 1 zeros between each of the original samples. Low-pass filter this signal at half of the lower of the two rates. Select every M-th sample from the filtered output, to obtain the result. Treat the samples as geometric points and create any needed new points by interpolation. Choosing an interpolation method is a trade-off between implementation complexity and conversion quality (according to application requirements). Commonly used are: ZOH (for film/video frames), cubic (for image processing) and windowed sinc function (for audio).