Fraser filter

A Fraser filter, named after Douglas Fraser, is typically used in geophysics when displaying VLF data. It is effectively the first derivative of the data.

If ${\displaystyle f(i)=f_{i}}$ represents the collected data then ${\displaystyle average_{12}={\frac {f_{1}+f_{2}}{2}}}$ is the average of two values. Consider this value to be plotted between point 1 and point 2 and do the same with points 3 and 4: ${\displaystyle average_{34}={\frac {f_{3}+f_{4}}{2}}}$

If ${\displaystyle \Delta x}$ represents the space between each station along the line then ${\displaystyle {\frac {average_{12}-average_{34}}{2\Delta x}}={\frac {(f_{1}+f_{2})-(f_{3}+f_{4})}{4\Delta x}}}$ is the Fraser Filter of those four values.

Since ${\displaystyle 4\Delta x}$ is constant, it can be ignored and the Fraser filter considered to be ${\displaystyle (f_{1}+f_{2})-(f_{3}+f_{4})}$.

References

Telford, W.M.; L.P. Geldart; R.E. Sheriff. Applied Geophyisics (2nd ed.).