Multiplication in the Fourier domain is convolution in the time domain.
Fourier-domain division is time-domain deconvolution.
In chapter we encountered the polynomial-division feedback operation
*X*(*Z*)=*Y*(*Z*)/*F*(*Z*).
This division is challenging when *F* has observational error.
By switching from the *Z*-domain to the -domain
we avoid needing to know if *F* is minimum phase.
The -domain has pitfalls too, however.
We may find for some real that vanishes,
so we cannot divide by that *F*.
Failure erupts if zero division occurs.
More insidious are the poor results we obtain
when zero division is avoided by a near miss.

- Dividing by zero smoothly
- Damped solution
- Example of deconvolution with a known wavelet
- Deconvolution with an unknown filter
- Explicit model for noise
- A self-fulfilling prophecy?

10/21/1998