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MAKE A MEME View Large Image $Filter Gain with Multiple Half-Sections.svg constant-k filter composed of n half-sections for n 1 2 3 4 5 10 20 with a cutoff frequency of 1 rad/s The transmission parameters of a single half-section are given by <math>\gamma \alpha + i ...$

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Keywords: Constant-k Filter Gain with Multiple Half-Sections.svg 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 <math>\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 </math> The gain of the whole filter is then <math>\mathrm H \omega \left e -\alpha \right n</math> own 2009-11-23 Inductiveload Mathematica Code <pre><nowiki> l 1; c 1; wc 1/Sqrtl c; gamw_ Piecewise I ArcSinw/wc w < wc ArcCoshw/wc + I Pi/2 w \GreaterSlantEqual wc gainw_ 1/ E Regamw; Plot Table gainw k k 1 2 3 4 5 10 20 w 0 2 PlotRange -> 0 1 </nowiki></pre> Constant-k filters