PAK Academy: Multi-Sampling to Reduce Aliasing Filter Requirements

A way to minimize the effect of aliasing is filtering the analog signal by means of a low-pass filter (see PAK Academy: Anti-Aliasing Filters). Such an analog filter is built out of electrical components, such as resistors and capacitors. In order to attenuate the frequency range above the Nyquist frequency sufficient enough, the slope after the cut-off frequency should be steep which means high order filters are required. This can only be realized with electrical components having very tight specifications, and are therefore very expensive.

Multi-Sampling for Anti-Aliasing

Moreover, as we are talking about electrical components with very tight specifications, the properties of the filter become temperature dependent due to slight variations in, for example, the resistance of the resistor. So in the past, users had to wait before their data acquisition systems had come to operating temperature to be able to use them.

Figure 1. shows the filter characteristics as used in the old days. The filter kicks in at about half of the sampling frequency. Aliasing effects caused by frequency content close to the sampling rate are minimized, but only to a certain extent.

Nowadays, these problems are circumvented by using a so called ‘Multi-Sampling Rate’ technique. Instead of sampling at slightly more than double the frequency range of interest (order of magnitude kHz), the analog signal is sampled much higher (order of magnitude MHz or GHz).

As a result, only frequency content close to the high sampling rate will mirror back into frequency content of interest. This allows the slope of the low-pass filter to be less steep (lower order filter) and therefore less electrical components with lower specifications are required.

Modern Techniques Use Extremely High Sampling Rates to Reduce Component Requirements in Data Acquisition Systems

This principle is shown in figure 2. Already a simple filter will reduce the contribution of the signal mirrored back into the signal.

A consequence is however that we are left with a high-sampled signal of which only a small frequency range is of interest. So obviously, the signal needs to be down sampled to an order of magnitude of kHz.

Down sampling consists of two steps:

  1. Low-pass filtering
  2. Sample decimation

The latter one is simply “throwing” away a large part of the samples. Each of the decimated samples would however still contain all the frequency content of the originally MHz / GHz sampling. It is therefore less simple as such.

Before decimation, it is essential to filter out the unwanted higher frequencies. This is again achieved by applying a low-pass filter. Indeed, for the same reason (aliasing) one needs to filter the analog signal before sampling, the digitized signal needs to be filtered before down sampling.

In other words, downsampling can be understood by realising that every time sample is in fact a summation of the contributions of every frequency component. By simple decimation (throwing samples away), these contributions are not lost and will cause aliasing effects in the down sampled signal. In order to reduce the higher frequency contributions, again a (digital) low-pass filter is required.

As the MHz / GHz signal is already in the digital domain, the low-pass filter is also a digital filter. The accuracy of the digital filter now only depends on the processors floating point accuracy. It is not temperature dependent and also (much) less expensive as the analog solution of the past.