Multi-rate digital signal processing

Sample-rate conversion is the process of changing the sampling rate of a discrete signal to obtain a new discrete representation of the underlying continuous signal. Application areas include image scaling, 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.

Within specific domains or for specific conversions, the following alternative terms for sample-rate conversion are also used: sampling-frequency conversion, resampling, upsampling, downsampling, interpolation, decimation, upscaling, downscaling. 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:

The two methods are mathematically identical: picking an interpolation function in the second scheme is equivalent to picking the impulse response of the filter in the first scheme. Linear interpolation is equivalent to a triangular impulse response; windowed sinc approximates a brick-wall filter (it approaches the desirable "brick wall" filter as the number of points increase). The length of the impulse response of the filter in method 1 corresponds to the number of points used in interpolation in method 2.

...
Wikipedia