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Let us take up a simple example
of **time-series analysis**.
Given the input, say , to some filter,
say , then the output is necessarily
.
To design an inverse filter,
we would wish to have **bold**c
come out as close as possible to (1, 0, 0).
So the statement of wishes (17) is
| |
(19) |

The method of solution is to premultiply by
the matrix , getting
| |
(20) |

Thus,
| |
(21) |

and the **inverse filter** comes out to be
| |
(22) |

Inserting this value of (*f*_{0},*f*_{1}) back into (19)
yields the actual output
,which is not a bad approximation to (1, 0, 0).

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Stanford Exploration Project

10/21/1998