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This is known as a moving average because the average at each k
th
instant is based on the most recent set
of n values. In other words, it is a moving window of n values that are used to calculate the average of the
data sequence (see Figure 1).
Figure 1: Moving Average of n Data Points
The averaging process can be improved if the calculations can be performed in a recursive fashion.
Equation 1 can also be represented as the previous total of n – 1 samples plus the new sample, and then
divided by n.
(3)
Using Equation 1, we can derive the equation for
(4)
This can be rearranged as shown in Equation 5:
(5)
Using Equation 5, we can replace the value of in equation 3 with
This yields Equation 6:
(6)
Equation 6 can be simplified to equation 7:
(7)
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