NYQUIST THEOREM

Introduction

The Nyquist theorem is a key concept in EEG that describes the minimum rate an EEG signal should be sampled to be accurately represented digitally.

Nyquist Theorem and Mathematical Basis

The Nyquist theorem states that in order to fully capture an EEG signal without loss of information, it must be sampled at a rate that is at least twice the maximum frequency in that particular signal.

Mathematically, the highest frequency that you wish to record,  ƒ_max and the sampling rate ƒ_sample, must satisfy:

ƒ_sample ≥ 2 × ƒ_max

For EEG, if we want to capture frequencies up to 70 Hz. Here 70 Hz represents ƒ_max. This means the minimum sampling rate needed is:

ƒ_sample = 2 × 70 Hz = 140 Hz

ACNS Guidelines for Sampling Rate

In practice, EEG systems will generally use higher than the minimum required sampling rate to accommodate for any unexpected high frequency components in the signal.

ACNS guidelines suggest that the sampling rate should be at least three times the high frequency filter setting. Most EEG machines have a high frequency filter set at 70 Hz, meaning that the minimum acceptable sampling rate according to ACNS guidelines should be 210 Hz. Understanding the difference between minimum sampling rate suggested by Nyquist theorem and the minimum sampling rate suggested by the ACNS guidelines will be important on test day.

Aliasing: When Nyquist Criterion Isn’t Met

Aliasing occurs when the sampling rate is below twice the highest frequency being recorded. Aliasing describes when high frequency signals are inaccurately represented as lower frequency components in the record. An example of this would be if a signal contains a 50 Hz (Gamma) component and the sampling rate is only 80 Hz, the 50 Hz signal would appear as a lower frequency. This is problematic as these benign gamma waves are misrepresented as beta waves leading to potential misinterpretation of the record. 

Figure 1 “Aliasing” Laurens R. Krol, CC0, via Wikimedia Commons

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