Chapter 5
Signal Generation Fundamentals
©
National Instruments Corporation
5-3
NI PXIe-5450 User Manual
Nyquist and Shannon's Sampling Theorems
The Nyquist theorem concerns digital sampling of a continuous time
analog waveform, while Shannon’s Sampling theorem concerns the
creation of a continuous time analog waveform from digital, discrete
samples.
Nyquist Theorem
The Nyquist theorem states that an analog signal must be sampled at least
twice as fast as the bandwidth of the signal to accurately reconstruct the
waveform; otherwise, the high-frequency content creates an alias at a
frequency inside the spectrum of interest (passband). An alias is a false
lower frequency component that appears in sampled data acquired at too
low a sampling rate. The following figure shows a 5 MHz sine wave
digitized by a 6 MS/s analog-to-digital converter (ADC). In this figure, the
solid line represents the sine wave being digitized, while the dotted line
represents the aliased signal recorded by the ADC at that sample rate.
The 5 MHz frequency aliases back in the passband, falsely appearing as a
1 MHz sine wave.
Shannon’s Sampling Theorem
Shannon’s Sampling theorem states that a digital waveform must be
updated at least twice as fast as the bandwidth of the signal to be accurately
generated. The same image that was used for the Nyquist example can be
used to demonstrate Shannon’s Sampling theorem.
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