Hardware and Functional Development of Protection Devices and Systems - Digital Signal Processing in Power System Protection and Control - page 22

Fig. 3.9 An illustration of sampling process in time and frequency domains

Fig. 3.10 Sampling of the fundamental and (sampling-fundamental) frequency signals

low-pass filter) only when the copies of original spectrum are separated one from
another, which coincides with the Shannon-Kotielnikov sampling theorem.
Another consequence of sampling can be seen in Fig. 3.10 . It can be observed
that for the sampling period T S = 2.5 ms, i.e. for the sampling frequency
f S = 400 Hz (8 samples per cycle of the fundamental 50 Hz component), both the
50 Hz signal and its reflected frequency component (400 - 50 = 350 Hz) after
sampling give exactly the same sampled values, in other words—they become
indistinguishable. If the signal contains both frequency components, then
depending on their phases the result of sampling would be a weighted sum/dif-
ference of both components. This is why the analog filtering is necessary—to filter
out the all components of frequencies higher than half of the sampling rate, and
thus eliminate the aliasing effects.
After sampling the signal becomes discretized in time, however, the values
remain still analog. For further processing they have to be represented in digital
form with finite number of digits, which is a role of an A/D converter. In modern
protective relays one A/D converter is used even if many channels for numerous
signals have to be processed. The A/D converter is then switched consecutively to
subsequent channels with use of a multiplexer and analog memory (usually a
capacitor bank), as shown in Fig. 3.11 .