The high-pass filter

The high-pass filter correction is obtained by multiplying the spectrum by [math]\displaystyle{ 1+\left( \frac{f_c}{f} \right)^2 }[/math] where [math]\displaystyle{ f_c }[/math] is the high-pass cut-off frequency and [math]\displaystyle{ f }[/math] is the frequency. The high-pass filter is assumed to be of single-pole, or first order, and has a transfer function of [math]\displaystyle{ \frac{j f/f_c}{1+jf/f_c} }[/math] where [math]\displaystyle{ j^2=-1 }[/math].