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 $f(i)=f_{i}$ represents the collected data then $average_{12}={\frac {f_{1}+f_{2}}{2}}$ 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: $average_{34}={\frac {f_{3}+f_{4}}{2}}$

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

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

References

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