Compute Allan variance for time series at given tau values.

PURPOSE
This app can be used to calculate Allan variance for a time series signal at given tau values. The output includes:

1. Allan deviation
2. Allan variance
3. Log-Log plot for Allan deviation

INSTALLATION
Download AllanVar.opx file, and then drag-and-drop onto the Origin workspace. An icon will appear in the Apps Gallery window.
NOTE: This tool requires OriginPro.

OPERATION

1. Create a worksheet and input data. Next activate the worksheet and click the Allan Variance icon in the Apps Gallery window.
2. In the opened dialog, select the XY data from the worksheet as Input Data. A value shown in Sampling Interval is automatically calculated according to your X data.  Uncheck the Auto check box to the right of Sampling Interval and specify a value if you don't want to use the calculated value.
3. tau Values Type provides two options: All and Custom. All option will calculate the result for tau values from 1 to one-half of the number of input points. Custom option will allow you to choose tau Values from the worksheet.
4. You can determine whether to show the Log-Log Plot for Allan deviation, and the destination for output results.

ALGORITHM
For input data y with N points, its time interval is dt, the Allan variance at \( \tau = k \ dt \) can be calculated as follows:

• Divide y into m subgroups, \(m = N/k\)
• Calculate the mean value in each subgroup.
• Calculate the difference for mean values in adjacent subgroups.
• Allan variance is half of the mean square of these difference values.

REFERENCE

1. P. Werle, R. Mucke, F. Slemr. The Limits of Signal Averaging in Atmospheric Trace-Gas Monitoring by Tunable Diode-Laser Absorption Spectroscopy (TDLAS). Applied Physics B 57, 131-139 (1993).

NOTE

1. This tool requires x data to be evenly spaced. If it is not, it will show a warning message at the bottom of the dialog. Precision error may cause ununiform x, and you can ignore the warning message caused by this error.
2. The Allan variance is calculated by the difference of values averaged over the measurement interval tau therefore phase data cannot be used in this tool directly.

v1.1 4/8/2019 Updated mean function.