Multidimensional autoregression |

man1
Top is known data.
Middle includes the interpolated values.
Bottom is the filter with the leftmost point constrained
to be unity
and other points chosen to minimize output power.
Figure 22. | |
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In Figure 22 the filter is constrained to be of the form . The result is pleasing in that the interpolated traces have the same general character as the given values. The filter came out slightly different from the that I guessed and tried in Figure . Curiously, constraining the filter to be of the form in Figure 23 yields the same interpolated missing data as in Figure 22. I understand that the sum squared of the coefficients of is the same as that of , but I do not see why that would imply the same interpolated data; never the less, it seems to.

man3
The filter here had its rightmost point constrained
to be unity--i.e., this filtering amounts to
backward prediction.
The interpolated data seems to be identical
to that of forward prediction.
Figure 23. | |
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Multidimensional autoregression |

2013-07-26