Downsampling

The term Down Sampling and downsampling (English ) refers to the reduction of the support points of a time series or other arrangements of discrete values ​​. Except for special cases, the downsampling is thereby connected with loss of information (as opposed to compression). It is the counterpart of the upsampling and as this is a special case of the resampling.

In raster graphics is referred to according to the reduction of the pixels ( samples ) than downsampling. However, the reduction of the bit depth for each color channel is nor downsampling such as reducing the bit depth of audio channels, because the number of samples remains the same. Downsampling therefore describes the process of a reduction in the time or spatial resolution ( audio and graphics ), a Bittiefenreduktionen a change of the quantization resolution.

Method

First, the time-discrete signal to prevent aliasing with an ideal low-pass filter ( sinc filter) is band-limited. The cutoff frequency of the low pass filtering, it is in the process of the actual loss of information is the Nyquist -Shannon sampling theorem, results, according to half the sampling frequency at the output. A downsampling with a previously performed low-pass filtering is referred to in the digital signal processing as decimation.

Special case Integer conversion factor

When the integer factor N is the ratio of high input clock frequency to lower output clock frequency, then every Nth value of the sequence is taken after the low-pass filtering to form the output sequence, the remaining values ​​in between are discarded.

Special case Rational conversion factor

Can the factor N expressed as a rational number in the form, you can initially set to the integer upsampling factor L performed subsequently downsampled to the integer factor M.

Any conversion factor

From a mathematical point of view, all resampling problems to Interpolationsprobleme of numerical mathematics for which it provides various methods, eg Nearest neighbor, linear or spline interpolation.

• Digital Signal Processing