Downsampling
The term downclocking or downsampling refers to the reduction of the support points of a time series or other arrangements of discrete values. With the exception of special cases, downsampling is associated with a loss of information (in contrast to compression ). It is the counterpart to upsampling and, like this, a special case of resampling .
In the case of raster graphics , the reduction in pixels ( samples ) is called downsampling. Reducing the bit depth of the individual color channels is just as little downsampling as reducing the bit depth of audio channels , since the number of samples remains the same. Downsampling describes the process of reducing the time or spatial resolution (audio or graphics), while a bit depth reduction describes a change in the quantization resolution .
Procedure
First of all, the time-discrete signal is band-limited with an ideal low-pass filter (sinc filter) to avoid aliasing effects . According to the Nyquist-Shannon sampling theorem , the cut-off frequency of the low-pass filtering, which represents the actual loss of information in the process, is half the sampling frequency at the output. Downsampling with previously performed low-pass filtering is also referred to as decimation in digital signal processing .
Special case: integer conversion factor
If the integer factor N is the ratio of high input clock frequency to a lower output clock frequency, then to form the output sequence of each is N th value of the sequence taken by the low-pass filtering, the remaining values in between are discarded.
Special case: rational conversion factor
The factor can be N as a rational number in the form of expressing, a can first upsampling to the integer factor M can be carried out, subsequently a down-sampling to the integer factor L .
Any conversion factor
From a mathematical point of view, all resampling problems are interpolation problems of numerical mathematics for which it provides various methods, e.g. B. Nearest neighbor, linear or spline interpolation.