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** Up:** PHASE OF A MINIMUM-PHASE
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Now let us sum up the behavior of phase of the **rational filter**

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By the rules of complex-number multiplication,
the phase of *B*(*Z*) is the sum of the phases in the numerator
minus the sum of the phases in the denominator.
Since we are discussing realizable filters,
the denominator factors must all be minimum-phase,
and so the denominator phase curve
is a sum of periodic phase curves
like the lower left of Figure 19.
The numerator factors may or may not be minimum-phase.
Thus the numerator phase curve is a sum of phase curves
that may resemble
either type in Figure 19.
If any factors augment phase by ,then the phase is not periodic,
and the filter is nonminimum-phase.

** Next:** ROBINSON'S ENERGY-DELAY THEOREM
** Up:** PHASE OF A MINIMUM-PHASE
** Previous:** Phase of a single
Stanford Exploration Project

10/21/1998