The *error* in prediction (or interpolation) is often more interesting
than the prediction itself.
When the predicted component is removed,
leaving the unpredictable, the residual is the prediction error.
Let us see how the program `shaper()` can be used
to find an interpolation-error filter like (*f _{-2}*,

(22) |

(*f _{-2}*,

Notice that the matrix in (22)
is *almost* **convolution**.
It would be convolution if the central column were not absent.
I propose that you not actually solve the system (22).
Instead I will show you a more general solution
that uses the convolution operator itself.
That way you will not need to write programs
for the many ``almost'' convolution operators arising
from the many PE and IE filters with their various **gap**s and **lag**s.

The conjugate-gradient program here is a combination
of earlier CG programs and the weighting methods we must introduce now:
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10/21/1998