This app can be used to calculate Allan variance for a time series signal at given tau values. The output includes:
- Allan deviation
- Allan variance
- Log-Log plot for Allan deviation
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.
- Create a worksheet and input data. Next activate the worksheet and click the Allan Variance icon in the Apps Gallery window.
- 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.
- 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.
- You can determine whether to show the Log-Log Plot for Allan deviation, and the destination for output results.
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.
- 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).
- 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.
- 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.