FOURIER TRANSFORM:
The importance of sampling rate
The importance of the sampling rate is demonstrated in the graphic to the right.
Realistic analogue signals are often modeled by the famous Fourier series as the summation of multiple sinusoids of different frequencies and amplitudes.
A transducer with low frequency response will not capture the high frequency signal, hence distorting the actual signal measured. If the number of samples is not properly chosen, one would end with several analogue functions for the same sample group other than the function these samples were taken from. Obviously this would make the reconstruction of the original sampled function ambiguous.
The graph above shows how two different sinusoids can fit the same set of samples. A transducer with higher sampling rate would convey signal more accurately than one with a lower sampling rate.
As was mentioned in the beginning …
this is the first of the eye-openers that would seriously
affect the choice of sensors and data processing peripherals such as on board electronics.
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