File:Elliptic Filter Response (4th Order).svg
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| Description |
English: The response of a 4-th order elliptic filter. Also shown is the maximum extent of the passband ripples, where ε is the ripple factor and Ln is the discrimination factor. |
| Date | |
| Source | Own work |
| Author | Inductiveload |
Mathematica Code
xp2[xi_] :=
Module[{g, num, den}, g = Sqrt[4*xi^2 + (4*xi^2*(xi^2 - 1))^(2/3)];
num = 2*xi^2*Sqrt[g];
den = Sqrt[8*xi^2*(xi^2 + 1) + 12*g*xi^2 - g^3] - Sqrt[g^3];
num/den];
xz2[xi_] := xi^2/xp2[xi];
t[xi_] := Sqrt[1 - 1/xi^2];
(*Use particular values for low-order functions*)
r1[xi_, x_] := x;
r2[xi_, x_] := ((t[xi] + 1)*x^2 - 1)/((t[xi] - 1)*x^2 + 1);
r3[xi_, x_] :=
x*((1 - xp2[xi])*(x^2 - xz2[xi]))/((1 - xz2[xi])*(x^2 - xp2[xi]));
(*Use nesting property for higher-degree functions*)
r4[xi_, x_] := r2[r2[xi, xi], r2[xi, x]];
ellgain[xi_, w_, w0_, ep_] := 1/Sqrt[1 + ep^2*r4[xi, w/w0]^2];
Plot[
ellgain[1.05, w, 1, 0.5],
{w, 0, 3}]
Licensing
|
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:26, 2 March 2025 | | 794 × 480 (3 KB) | Д.Ильин | Optimization |
| 05:54, 29 January 2009 |  | 720 × 460 (70 KB) | Inductiveload | added ξ line | |
| 05:40, 29 January 2009 |  | 720 × 460 (68 KB) | Inductiveload | {{Information |Description={{en|1=The response of a 4-th order en:elliptic filter. Also shown is the maximum extent of the passband ripples, where ''ε'' is the ripple factor and ''L''<sub>n</sub> is the discrimination factor.}} |Source=Own w |
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