File:Elliptic Filter s-Plane Response (8th Order).svg
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DescriptionElliptic Filter s-Plane Response (8th Order).svg |
English: Log-absolute complex frequency (s=σ+jω) response of an 8th order elliptic filter. Values less than 0.0001 are black; greater than 10 are in white.
ξ = 1.05, ε = 0.5 and ω0 = 1. |
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Date | ||||
Source | Own work | |||
Author | Inductiveload | |||
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Mathematica Code
[edit]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]]; r8[xi_, x_] := r4[r2[xi, xi], r2[xi, x]]; ellgain[xi_, w_, w0_, ep_] := 1/Sqrt[1 + ep^2*r8[xi, w/w0]^2]; DensityPlot[ w0 = 1; ep = 0.5; xi = 1.05; min = 0.0001; max = 10; Log[Abs[ ellgain[xi, sig + I*w, w0*I, ep] ]], {sig, -4, 4}, {w, -4, 4}, PlotRange -> {Log[min], Log[max]}, PlotPoints -> 100, ColorFunction -> GrayLevel, ClippingStyle -> {Black, White} ]
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 22:47, 30 January 2009 | ![]() | 480 × 460 (352 KB) | Inductiveload (talk | contribs) | {{Information |Description={{en|1=Log-absolute complex frequency (''s''=''σ''+''jω'') response of an 8th order en:elliptic filter. Values less than 0.0001 are black; greater than 10 are in white. ''ξ'' = 1.05, ''ε'' = 0.5 and ''ω' |
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