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Data Revival from the Statistics
In the previous example, we have the following results:
Suppose we only stored all the time-average data. Can we get back the
real measurement data only based on the stored time-average? Yes, we
can revive the measurement data only based on the time-average, provided
we know the sequence data number Remember that we have recursive formula (3) to compute the time-average. I write it again in here for your convenient: Rearrange the equation (3) for As before, the subscript
To restore data from the statistics using equation (5) above, we need
to know the sequence data number Yes, we can revive the real measurement data from two consecutive time average and time variance using the following formula where, Using previous example, we have the statistics (time average and time variance) and we can revive the data. Obviously, we use quadratic formula to get the data, thus two possible value are the results.
Note that the only first measurement data is revived using positive sign of equation (6), while the others revival measurement data are obtained using the negative sign. This rule is true for any measurement data.
See proof of the quadratic formula here
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