Engineering

## Analogue to Digital Conversion [PART 3 – Aliasing]

(Continuation from Part 2)

When choosing sampling rate, caution must be taken to avoid aliasing. This is a phenomenon whereby at low sampling rates, some of the higher frequencies present in a signal may be incorrectly detected as lower frequencies. Again, a great way to visualise this is through an example. If we look at the red sine wave in Figure 1 below, we can see that it has a frequency of   1/(pi/2) = 0.64 Hz. If sampled at a frequency of 2/((2*pi)/3) = 0.48 Hz, which is lower than the frequency in question, then the sample points wouldn’t be enough to reconstruct the wave. Instead, if we try to reconstruct it, we would see another sine wave (blue) which is a lower harmonic of the one in question. This happens because when we sample the signal at two or fewer times per cycle, it results in missed cycles, giving the illusion that a different (lower frequency) signal is being measured.

Figure 1 – Aliasing of Signal

To avoid this, sampling must be done with a frequency of at least 2 times the frequency of interest. This is known as the Nyquist frequency.

A useful method of ensuring that frequencies above the Nyquist frequency are avoided is by filtering the input of the ADC with a low-pass filter. This will allow frequencies lower than the cut-off frequency to pass, and attenuate anything higher. The degree of attenuation depends on the design of the low pass filter.

Low pass filters vary in design, but at its simplest it can be just a series resistor with a parallel capacitor. At low frequencies, due to the reactance of the capacitor, signals are forced through the load. At high frequencies, the capacitor acts as a short circuit. The cut-off frequency is given by the following relationship:

Seen in Figure 2 below is an example of a basic low pass filter:

Figure 2 – Low-Pass Filter

Another way of reducing aliasing is by Oversampling. This will be covered in more depth later, but essentially signals can be sampled at a rate much higher than the Nyquist frequency and then, for economy, digitally filtered back to the signal bandwidth. This will also make the design of the low-pass filter much easier and more economical, as now, we do not require a very sharp and very accurate cut-off frequency. With today’s processor speeds, oversampling is easily achievable for most applications. It is very common, as for no extra cost, it provides a very effective way of avoiding aliasing (amongst other benefits that will be covered later).