misif90
Figure 22 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. |
In Figure the filter is constrained to be of the form (1,a_{1},a_{2}). 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 (1,0,-1) that I guessed and tried in Figure . Curiously, constraining the filter to be of the form (a_{-2},a_{-1},1) in Figure yields the same interpolated missing data as in Figure . I understand that the sum squared of the coefficients of A(Z)P(Z) is the same as that of A(1/Z)P(Z), but I do not see why that would imply the same interpolated data; never the less, it seems to.
backwards90
Figure 23 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. |