Spencer's Formula
Define the notation
![[n]f_0=f_(-(n-1)/2)+...+f_0+...+f_((n-1)/2)](/images/equations/SpencersFormula/NumberedEquation1.gif) |
(1)
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and let 
be the central difference, so
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(2)
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Spencer's 21-term moving average formula is then given by
![f_0^'=([5][5][7])/(5·5·7)(1-4delta^2)f_0,](/images/equations/SpencersFormula/NumberedEquation3.gif) |
(3)
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which, written explicitly, gives
![f_0^'=1/(350)[60f_0+57(f_(-1)+f_1)+47(f_(-2)+f_2)+33(f_(-3)+f_3)+18(f_(-4)+f_4)+6(f_(-5)+f_5)-2(f_(-6)+f_6)-5(f_(-7)+f_7)-5(f_(-8)+f_8)-3(f_(-9)+f_9)-(f_(-10)+f_(10))]](/images/equations/SpencersFormula/NumberedEquation4.gif) |
(4)
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Spencer's Formula
Define the notation
and let
Spencer's 21-term moving average formula is then given by
which, written explicitly, gives
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