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Given different numerical values for *Z*, we can ask
whether *X*(*Z*) is finite or infinite.
Numerical values of *Z* of particular interest are
*Z* = +1, *Z* = -1, and
all those complex values of *Z* which are unit magnitude,
say |*Z*| = 1 or ,where is the real Fourier transform variable.
When is the variable, the *Z*-transform is a Fourier sum.
We can restrict our attention to those signals *u*_{t}
that have a finite
amount of energy by demanding that *U*(*Z*) be
finite for all values of *Z* on the unit circle |*Z*| = 1.
Filter functions always have finite energy.

** Next:** Causality and the unit
** Up:** INSTABILITY
** Previous:** The meaning of divergence
Stanford Exploration Project

10/21/1998