# The Nyquist Sampling Theorem

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• Preventing high frequency noise from being aliased to lower frequency measurements

Aliasing can only be prevented by suppressing high frequency information. If a waveform is a sum of a 1 KHz and a 12 KHz component, sampling at 7 KHz will give the 1 KHz component directly and alias the 12 KHz component to 1.5 KHz (Nyquist frequency 3.5 KHz; 3rd harmonic of the Nyquist frequency is at 10.5 KHz, so the aliasing is at 12 KHz - 10.5 KHz = 1.5 KHz). As we have said several times on this page, there is no way after sampling has occurred to tell if the 1.5 KHz component (or, for that matter, the 1 KHz component!) is real or aliased. Thus, one requires an anti-aliasing filter or an electronic device to limit the range of frequencies reaching the digitizer to suppress signals outside the unaliased range one wishes to observe. Alternately, one might suppress frequencies outside a narrow range (including suppressing low frequencies) so that one can INTENTIONALLY alias a high frequency signal into the range of a low frequency digitizer. One can then reconstruct the true waveform from knowledge of the sampled waveform and the anti-aliasing filter's throughput properties. By far the most common approach is to use a low-pass filter (a filter that lets through DC and slowly changing signals) to block high frequency noise and interfering signals. The design of such filters is outside the scope of this module. That such filters MUST be used should be evident, based on the discussion and exercises above.