Nyquist frequency

Download

• Nyquist frequency.vi - LabVIEW Virtual Instrument (requires LabVIEW version 2010 or higher)

• Nyquist frequency.exe - Stand-alone executable (download folder and run setup.exe to install)

• JavaScript version - runs directly in web browser

Description

The Nyquist sampling theorom states that, in digitally reproducing an analog signal, the digital sampling rate must be at least twice the highest frequency (f) of the components making up the analog signal.  The Nyquist frequency is then 2f, so the sampling frequency must be at least 2f = 1/Dt where Dt is the time interval between signal samples.  As the sampling frequency drops below the Nyquist frequency, the digital signal begins to show frequency components that differ from the original, an effect known as aliasing. 

This simulation generates a sine wave with user-defined frequency (f) and amplitude, along with a background of Gaussian white noise.  The user sets the sampling rate for the digital signal, and both the analog and digital signals are displayed.  Aliasing can be seen as the sampling frequency drops below the Nyquist frequency (2f).  Also, it can be seen that features of the analog signal are lost when the sampling frequency drops below ~20f. 

(Reference: Skoog, Holler, and Crouch, Principles of Instrumental Analysis, 6th Ed Thomson Brooks/Cole 2007)

Front panel

Guiding questions

Use an analog signal with a frequency of 10 and amplitude of 5 to answer the following.

• 1. What is the minimum sampling rate you should use as determined by the Nyquist Sampling Theorem?

  2. Using this sampling rate, what are the differences between the analog and the digital signals?

  3. What do you notice as the sampling rate drops below the Nyquist frequency?

  4. With no noise on the analog signal, at what sampling frequency does the shape of the digital signal begin to differ significantly from the analog signal?

  5. Now add noise with a level of 3.  How does your answer to question 4 change?