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Consider a system with an impulse response (2,-1,-1).
Its *Z*-transform is *B*(*Z*) = 2 - *Z* - *Z*^{2}.
This polynomial can be **factor**ed into .Thus our original filter could be thought of as a cascade
of two filters, (2,1) and (1,-1).
Either of the two filters could be applied first and the other second:
the output would be the same.
Since any polynomial can be factored,
any impulse response can be simulated by a cascade of two-term filters
(impulse responses whose *Z*-transforms are linear in *Z*).

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Stanford Exploration Project

10/21/1998