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Given inputs and outputs,
the problem of finding an unknown filter appears to be overdetermined,
so we write where the matrix is a matrix of downshifted columns like
(19).
Thus the quadratic form to be minimized
is a restatement of equation (25)
using filter definitions:
| |
(27) |

The solution is found just as we found
(26),
and it is the set of simultaneous equations
.

** Next:** Unknown input: deconvolution with
** Up:** Time domain versus frequency
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Stanford Exploration Project

10/21/1998