Ensemble averaging

Download

• • Ensemble averaging.vi - LabVIEW Virtual Instrument (requires LabVIEW version 2010 or higher)

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

  • JavaScript version - runs directly in web browser

Description

In ensemble averaging, n sets of data are obtained and averaged together to reduce random fluctuations in the signal.  The signal-to-noise ratio (S/N) is proportional to the square root of the number of scans (n1/2).

In this simulation 200 points of Gaussian white noise are generated, and a user-defined "signal" level is added to point #100.  The entire array is plotted and the S/N ratio is calculated by dividing the new value of point #100 by the standard deviation of the noise.  This process is repeated n times at a user-defined rate.  After each iteration (scan), an average of all scans is displayed, along with the overall S/N ratio and a plot of S/N vs n1/2.

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

Front panel

Guiding questions

• 1. With a signal level of 4, how many scans does it take to reach an overall S/N value of 40?  Repeat this three times and report your values.  How does this compare to theory?

  2. With a signal level of 0.4, how many scans does it take to reach an overall S/N value of 40?  Repeat this three times and report your values?  How does this compare to theory?