Boxcar Averaging
- Page ID
- 77550
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Boxcar averaging is a data treatment method that enhances the signal-to-noise of an analytical signal by replacing a group of consecutive data points with its average. This treatment, which is called smoothing, filters out rapidly changing signals by averaging over a relatively long time but has a negligible effect on slowly changing signals. Therefore, boxcar averaging mimics a software- based low-pass filter. Boxcar averaging can be done both in real time and after data acquisition is complete.
How Boxcar Averaging Works
During Data Acquisition:
- The signal is sampled several times. Theoretically, any number of points may be used.
- The samples are summed together and an average is calculated.
- The average signal (dependent variable) is stored in the smoothed data set as the y-coordinate, and the average value of the independent variable (e.g. time, wavelength) is used as the x-coordinate.
After Data Acquisition (see figure below):
- Sum the data points within the boxcar
- Divide by the number of points in the boxcar
- Plot the average y-value at the central x-value of the boxcar
- Repeat with Boxcar 2, etc until the last full boxcar is smoothed
Main Points about Boxcar Averaging
- Boxcar averaging is equivalent to software-based low-pass filtering.
- Boxcar averaging is straightforward to implement.
- Improvement in S/N is proportional to:
\[\sqrt{\textrm{# of data points in boxcar}}\]
- (N-1) points are lost from each boxcar in the smoothed data set, where N is the boxcar length. The data density of the smoothed data set will be reduced by (N-1)/N
- Significant loss of information can occur if the length of the boxcar is comparable to the data acquisition rate. It is best to implement boxcar averaging with a sufficient data acquisition rate.
Example of Boxcar Averaging
- There are two 5 μV signals below
- Peak at 1.00 minutes with a width of 0.04 minutes
- Peak at 2.00 minutes with a width of 0.40 minutes
- Levels of boxcar averaging are as follows
- Bottom dataset: Theoretical S/N of 13 (no smoothing)
- Middle dataset: Theoretical S/N of 29 (Five-point boxcar, 0.05 min long)
- Top dataset: Theoretical S/N of 39 (Nine-point boxcar, 0.09 min long)
- Notice that little distortion occurs if the peak width is much larger than the boxcar and significant S/N enhancement is possible.
- Signals with frequencies similar to the rate of data acquisition are quickly attenuated, analogous to a low-pass RC filter.
- Click here to work on a boxcar averaging exercise.