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(This section is a heavy rewrite of classical material
with a surprising twist near the end).
Multiplication in the Fourier domain is convolution in the time domain.
Division is deconvolution.
We have already encountered the polynomial-division feedback operation
*X*(*Z*)=*Y*(*Z*)/*F*(*Z*).
The division is challenging when *F* has observational error.
First by switching from the *Z*-domain to the -domain
we avoid needing to know if *F* is minimum phase.
But the -domain has pitfalls too.
We may find for some real that vanishes
so we cannot divide by that *F*.
Failure erupts if zero-division occurs.
More insidiously,
when zero-division is avoided by a near miss,
then results turn out poor.

** Next:** Dividing by zero smoothly
** Up:** Univariate problems
** Previous:** Univariate problems
Stanford Exploration Project

1/13/1998