Fraser Filter

A Fraser Filter 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 \((f_1 + f_2)-(f_3 + f_4)\).