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 $$(f_1 + f_2)-(f_3 + f_4)$$.