Upsampling

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In the context of digital signal processing, the term upsampling or sampling rate increase describes the conversion of a digital signal with a low sampling rate to a digital signal with a higher sampling rate, the signal information being retained completely and unchanged. Upsampling is the opposite of downsampling and is a form of sample rate conversion based on the mathematical function of interpolation .

Procedure

Special case: integer interpolation factor

Upsampling by the interpolation factor L = 3

The upsampling is characterized by the integer interpolation factor L , which expresses the ratio of the higher sampling rate of the sequence y [n] at the output to the lower sampling rate of the input sequence x [n]. The process is two-stage, as shown in the figure on the right using an exemplary signal curve:

  1. First, the input sequence x [n] with a low sampling rate is converted into a sequence v [n] with a higher sampling rate. For this purpose, between the individual sampling values, shown in the figure in the form of black dots, additional gray sampling values ​​are supplemented with the value 0. With an interpolation factor of L = 3, for example, two additional values ​​with the value 0 are always inserted between two sample values.
  2. The sequence v [n] formed in this way is passed through a low-pass filter which has the so-called Nyquist frequency of the input sequence x [n] as the cutoff frequency . This low-pass filter is implemented as a digital filter and uses interpolation to form the output sequence y [n] from the sequence v [n].

Special case rational interpolation factor

In a non-integer interpolation factor, which is in the form , ie as a rational number can be expressed, In the simplest case, first an upsampling by a factor L followed by downsampling by a factor M .

Any interpolation 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, Lineare- or spline - interpolation .

literature

  • Alan V. Oppenheim, Ronald W. Schafer: Discrete-time signal processing . 3. Edition. Oldenbourg, 1999, ISBN 3-486-24145-1 .