Essential mathematics
When computers are used to control engineering systems, the best they can do is to take occasional snapshots or samples of events. Provided events are changing slowly and the computer is sampling rapidly, Shannon’s sampling rule will be satisfied. It will be possible to recover the digitally processed signal without corruption attributable to aliasing.
To illustrate the potential hazards of periodic sampling, visualize a rotating radar scanner tracking the progress of an approaching aircraft. The air traffic controller patiently monitoring a flickering cathode-ray tube might observe a steady approach when the flight path could in fact be wavering, vertically and horizontally, about its ideal projected path. Because the ...
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