# Digital calculations

Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 9 295 - 366 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store

## Problem

Fill in the values in Table 9.9a.

### Solution

Table 9.9b shows Table 9.9a completed.

Table 9.9a. Digital wavelets and operations.
${\displaystyle t=-3}$ ${\displaystyle t=-2}$ ${\displaystyle t=-1}$ ${\displaystyle t=0}$ ${\displaystyle t=+1}$ ${\displaystyle t=+2}$ ${\displaystyle t=+3}$ ${\displaystyle t=+4}$ ${\displaystyle t=+5}$
${\displaystyle a_{t}=\left[2,\;1\;,\;-2,\;1\right]}$
${\displaystyle b_{t}=-2a_{t}}$
${\displaystyle c_{t}{=3a_{t-2}}}$
${\displaystyle {\hbox{d}}_{t}{=a_{-t}}/2}$
${\displaystyle e_{t}=\pi a_{3-t}}$
${\displaystyle f_{t}=\left[-1,\;1\right]}$
${\displaystyle g_{t}{=a_{t}*f_{t}}}$
${\displaystyle \delta _{t+2}}$
${\displaystyle \delta _{2-t}}$
${\displaystyle \phi _{ff}(t)}$
${\displaystyle \phi _{fa}(t)}$
Table 9.9b. Completed table.
${\displaystyle t=-3}$ ${\displaystyle t=-2}$ ${\displaystyle t=-1}$ ${\displaystyle t=0}$ ${\displaystyle t=+1}$ ${\displaystyle t=+2}$ ${\displaystyle t=+3}$ ${\displaystyle t=+4}$ ${\displaystyle t=+5}$
${\displaystyle a_{t}=\left[2,\;1\;,\;-2,\;1\right]}$ 0 0 0 2 1 ${\displaystyle -2}$ 1 0 0
${\displaystyle b_{t}=-2a_{t}}$ 0 0 0 ${\displaystyle -4}$ ${\displaystyle -2}$ 4 ${\displaystyle -2}$ 0 0
${\displaystyle c_{t}{=3a_{t-2}}}$ 0 0 0 0 0 6 3 ${\displaystyle -6}$ 3
${\displaystyle {\hbox{d}}_{t}{=a_{-t}}/2}$ 1/2 ${\displaystyle -1}$ 1/2 1 0 0 0 0 0
${\displaystyle e_{t}=\pi a_{3-t}}$ 0 0 0 ${\displaystyle \pi }$ ${\displaystyle -2\pi }$ ${\displaystyle \pi }$ ${\displaystyle 2\pi }$ 0 0
${\displaystyle f_{t}=\left[-1,\;1\right]}$ 0 0 0 ${\displaystyle -1}$ 1 0 0 0 0
${\displaystyle g_{t}{=a_{t}*f_{t}}}$ 0 0 0 ${\displaystyle -2}$ 1 3 ${\displaystyle -3}$ 1 0
${\displaystyle \delta _{t+2}}$ 0 1 0 0 0 0 0 0 0
${\displaystyle \delta _{2-t}}$ 0 0 0 0 0 1 0 0 0
${\displaystyle \phi _{ff}(t)}$ 0 0 ${\displaystyle -1}$ 2 ${\displaystyle -1}$ 0 0 0 0
${\displaystyle \phi _{fa}(t)}$ 0 0 0 ${\displaystyle -1}$ ${\displaystyle -1}$ ${\displaystyle -3}$ 3 ${\displaystyle -1}$ 0