Sample rate conversion

The sample rate conversion (English Sample rate conversion or resampling ), within the context of digital signal processing, the implementation of a digital signal between two different sampling rates below as complete as possible while maintaining the signal information. In the field of digital image processing raster graphics, this process is referred to as scaling.

General

, The reaction of a high sampling rate to a lower sampling rate, this is also referred to as down-sampling ( decimation ), the reverse reaction of a low sampling frequency to a high sampling rate is referred to as up-sampling (interpolation). In order to destroy the information in the signal as little as possible, must be observed at the sampling rate conversion, the Nyquist -Shannon sampling theorem. This means in particular that frequency components in the signal must not be above the Nyquist frequency of the lower sampling rate in order to avoid spurious effects as aliasing.

For example, for audio CDs, a sampling rate of 44.1 kHz is used, however, at the Digital Audio Tape (DAT ) is a common and in the studio area and broadcasters sampling rate of 48 kHz. Both sampling rates are sufficient to detect audio signals with frequencies up to 20 kHz. The sampling rate conversion is necessary for example when re-recordings between the two sampling rates.

In the adjacent figure in the time domain, an exemplary waveform with two signal sequences with different sampling rates, shown in red and green with a low sampling rate with a higher sampling rate. The information of the signal, stored in light gray is, in both cases ident If the waveform with the lower sampling 1/Tsb (in red) before, so by interpolation between the values ​​with the new, higher sampling 1/Tsa ( in green) formed. The process of interpolation is also provide the calculation of intermediate values ​​by means of digital filters which in addition to the necessary bandwidth limitation to fulfill the Nyquist criterion. Those digital filter count, since they operate at different sampling rates, to the multi-rate filter. An example of a simple filter for synchronous sample rate conversion represents the cascaded integrator -comb filter (CIC ) filter

Species

The sample rate conversion is made between two main application areas:

• Synchronous sampling rate conversion ( SRC) with nominal different but temporally fixed sampling rates. This is normally the case when, are formed from a clock source both sampling rates, such as single and double sampling. Through system-related deviations and tolerances of the clock source both sampling rates change so in the same proportion and the relation between the two sampling time is fixed.
• Asynchronous sample rate conversion ( ASRC ) with temporally fixed sampling rates. It may, but need not, be the different sample nominally equal. This is for example the case when two independent clock sources are used for generating the sampling frequency. The slightest deviations and ever-present, for example, according to temperature effects, it is also at this same nominal clock speeds at minimal deviations that would, after some time to skip or duplicate of one sample and thus lead to errors. The case of the asynchronous sampling rate conversion is technically more complicated.

In synchronous sample rate conversion in advance the exact date is always known where a particular sample must be calculated on the time axis. With asynchronous sampling rate conversion, this is not possible. In this case, additional necessary control loops are used (English Digital servo loops) controlled by means of current -time measurements between the two sampling rates and formed therefrom error signals, which make the current readjustment and change the filter coefficients in the interpolation. Typically, a polyphase filter banks come in to apply. The sample may not approach too fast change over time, to ensure tracking of the controlled system.