Nyquist Theorem: Why Sampling Frequency Matters

According to the Nyquist theorem, to accurately determine a periodic signal’s true frequency, we must sample the signal at least twice during each cycle or period. If we collect samples at an interval of Δt, the highest frequency we can monitor accurately is (2Δt)–1. For example, if our sampling rate is 1 sample/hr, the highest frequency we can monitor is (2×1 hr)–1 or 0.5 hr–1, corresponding to a period of less than 2 hr. If our signal’s period is less than 2 hours (a frequency of more than 0.5 hr–1), then we must use a faster sampling rate. Ideally, the sampling rate should be at least 3-4 times greater than the highest frequency signal of interest. If our signal has a period of one hour, we should collect a new sample every 15-20 minutes.

Effect of sampling frequency when monitoring a periodic signal is demonstrated in this figure. Individual samples are shown by the red dots (). In (a) the sampling frequency is approximately 1.5 samples per period. The dashed red line shows the apparent signal based on five samples and the solid blue line shows the true signal. In (b) a sampling frequency of approximately 5 samples per period accurately reproduces the true signal.

Figure7.4

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