Figure 4: Noisy and noise free evolution of the cell pseudo-resistance
The first question that comes to mind, considering the nature of a noisy signal, is
what would be the appropriate data sampling rate and is the moving average calculation
helpful in decreasing this type of noise?
To remove the noise having a frequency of about 0.008 Hz, it is required to
perform moving average calculations over a span of at least 2 minutes, which means
more than 1200 data points if a 10 Hz data sampling rate is used. As can be seen in
Figure 5, the higher frequency noise is almost completely removed and the resulting red
curve is a good fit of the blue curve in Figure 4.
Notice that the red curve locates the calculated average voltage at the average
time which means that the last calculated value was the average voltage 1 minute ago.
The black curve is the moving average curve the way Excel presents it, which is
incorrect. In order to assess the averaged or smoothed value at the time of the last data
point collected (which is assumed to be the present time), an extrapolation of the red
curve would need to be performed which would require some kind of data fitting.
Moving averages can also be used to reduce the number of data points to perform
data fit calculations. For example, collecting 10 Hz and saving only the 6 seconds
moving averaged values every 6 seconds. This would remove very high frequency noise
of 0.2 Hz and higher so it would remove CO
2
gas bubble release noise which is estimated
to be about 1 Hz (see Figure 6).