** Next:** Crosscorrelation
** Up:** CORRELATION AND SPECTRA
** Previous:** Time-domain conjugate

Filters
are often used to change the spectra of given data.
With input *X*(*Z*),
filters *B*(*Z*), and output *Y*(*Z*), we have
*Y*(*Z*) = *B*(*Z*)*X*(*Z*) and the Fourier conjugate
.
Multiplying these two relations together, we get
which says that the spectrum of the input times the spectrum
of the filter equals the spectrum of the output.
Filters are often characterized by the shape of their spectra;
this shape is the same as the
**spectral ratio**
of the output over the input:
| |
(47) |

** Next:** Crosscorrelation
** Up:** CORRELATION AND SPECTRA
** Previous:** Time-domain conjugate
Stanford Exploration Project

10/21/1998