English: A graph of the gain of a lowpass constant-k filter composed of n half-sections (for n = 1,2,3,4,5,10,20), with a cutoff frequency of 1 rad/s. The transmission parameters of a single half-section are given by:

${\displaystyle \gamma =\alpha +i\beta ={\begin{cases}0+\sin ^{-1}{\frac {\omega }{\omega _{c}}},&\omega <\omega _{c}\\\cosh ^{-1}{\frac {\omega }{\omega _{c}}}+i{\frac {\pi }{2}},&\omega >\omega _{c}\end{cases}}}$

The gain of the whole filter is then:

${\displaystyle \mathrm {H} (\omega )=\left(e^{-\alpha }\right)^{n}}$