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Spectral transfer function

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 $\overline{Y}(1/Z) = \overline{B}(1/Z) \overline{X}(1/Z)$. Multiplying these two relations together, we get
\begin{displaymath}
\overline {Y} Y \eq (\overline{B} B)(\overline{X} X) \nonumber\end{displaymath}   
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:
\begin{displaymath}
\overline{B} B \eq
{\overline {Y} Y \over \overline{X} X }\end{displaymath} (47)

next up previous print clean
Next: Crosscorrelation Up: CORRELATION AND SPECTRA Previous: Time-domain conjugate
Stanford Exploration Project
10/21/1998