Nyquist Theorem

NI High-Speed Digitizers Help (NI-SCOPE)

Edition Date: January 2017

Part Number: 370592AB-01

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The Nyquist theorem states that a signal must be sampled at least twice as fast as the highest frequency component of the signal to accurately reconstruct the waveform. Frequency components higher than half the sample rate are mistakenly interpreted as low-frequency components, a phenomenon known as aliasing. The following figure shows a 5 MHz sine wave digitized by a 6 MS/s ADC. The dotted line indicates the aliased signal recorded by the ADC at that sample rate. The 5 MHz frequency aliases back into the passband, falsely appearing as a 1 MHz sine wave. Inserting a lowpass filter with a cutoff at the Nyquist rate prevents aliasing in the passband.

The following figure shows the frequency view of the same example.


fs = 6 MS/s
fN = 3 MHz (the Nyquist frequency)
fa = 1 MHz (1fs - 5 MHz)

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