Sample rate conversion

from Wikipedia, the free encyclopedia

The sampling rate conversion ( English sample rate conversion or resampling ) describes in the context of digital signal processing the conversion of a digital signal between two different sampling rates while retaining the signal information as completely as possible. In the field of digital image processing of raster graphics , this process is also known as scaling .

General

Exemplary signal curve in the time domain in gray and, derived from this, two time-discrete signal sequences with different sampling rates in red and green

If the conversion takes place from a high sampling rate to a lower sampling rate, this is also referred to as downsampling (decimation), the reverse conversion from a low sampling rate to a high sampling rate is referred to as upsampling (interpolation). In order to falsify the information in the signal as little as possible, the Nyquist-Shannon sampling theorem must be observed when converting the sampling rate . 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 interference effects such as the aliasing effect .

For example, a sampling rate of 44.1 kHz is used for audio CDs , whereas for digital audio tape (DAT) a sampling rate of 48 kHz, which is also used in studios and broadcasters. Both sampling rates are sufficient to capture audio signals with frequencies of up to 20 kHz. The sampling rate conversion is necessary, for example, when transferring between the two sampling rates.

The figure on the right shows an example signal curve in the time domain with two signal sequences with different sampling rates, red with a lower sampling rate and green with a higher sampling rate. The information of the signal, highlighted in light gray, is identical in both cases. If the signal curve is available with the lower sampling rate 1 / Tsb (in red), then the intermediate values with the new, higher sampling rate 1 / Tsa (in green) are generated by means of interpolation . The interpolation process is carried out using digital filters which, in addition to the band limitation required to meet the Nyquist criterion, also provide the calculation of the intermediate values. Since they work with different sampling rates, those digital filters count as multi-rate filters. An example of a simple filter for synchronous sample rate conversion is the cascaded integrator comb filter (CIC filter).

species

A distinction is made between two main areas of application for sample rate conversion:

  • Synchronous sampling rate conversion (SRC) with nominally different but temporally fixed sampling rates. This is usually the case when both sampling rates, for example single and double sampling rates, are generated by a clock source . Due to system-related deviations and tolerances of the clock source, both sampling rates change in the same ratio and the relation between the two sampling rates is fixed over time.
  • Asynchronous sampling rate conversion (ASRC) with sampling rates that are not fixed in time. The different sampling rates can, but need not, be nominally the same. This is the case, for example, when two independent clock sources are used to generate the sampling frequency. As a result of minimal and always present deviations, for example as a result of temperature influences, there are minimal deviations, even with nominally identical clock rates, which after some time would lead to skipping or duplicating a sample and thus to errors. The case of asynchronous sample rate conversion is technically more complex.

With synchronous sampling rate conversion, the exact point in time is always known in advance at which a certain sampling value has to be calculated on the time axis. This is not possible with asynchronous sample rate conversion. In this case, by means of operating-time measurements between the two sampling rates and formed therefrom error signals necessary additional control loops ( English digital servo loop ) control which make the current readjustment and changing the filter coefficients in the interpolation filters. Typically, filter banks with a polyphase structure are used. The sampling rates must not change over time too quickly in order to ensure that the controlled system is updated.

Individual evidence

  1. ↑ AD1895 Audio Asynchronous Sample Rate Converter (PDF; 875 kB), data sheet, Analog Devices, 2002 (engl.)

literature