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 [math]\displaystyle{ f(i) = f_i }[/math] represents the collected data then [math]\displaystyle{ average_{12}=\frac{f_1 + f_2}{2} }[/math] 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: [math]\displaystyle{ average_{34}=\frac{f_3 + f_4}{2} }[/math]

If [math]\displaystyle{ \Delta x }[/math] represents the space between each station along the line then [math]\displaystyle{ \frac{average_{12}-average_{34}}{2 \Delta x}=\frac{(f_1 + f_2)-(f_3 + f_4)}{4 \Delta x} }[/math] is the Fraser Filter of those four values.

Since [math]\displaystyle{ 4 \Delta x }[/math] is constant, it can be ignored and the Fraser Filter considered to be [math]\displaystyle{ (f_1 + f_2)-(f_3 + f_4) }[/math].

References

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