EllipticFilterModel
EllipticFilterModel
设计阶数为 n 的低通椭圆滤波器.
EllipticFilterModel[{n,ωc}]
使用截止频率 ωc.
EllipticFilterModel[{"type",spec}]
使用 spec 设计具有指定类型 "type" 的椭圆滤波器.
EllipticFilterModel[{"type",spec},var]
以变量 var 表示模型.
更多信息
- EllipticFilterModel 以 TransferFunctionModel 的形式返回设计的滤波器.
- EllipticFilterModel[{n,ω}] 在频率 ω 处返回衰减量为
(约为 3 dB）的低通滤波器. - EllipticFilterModel[n] 使用截止频率1.
- 滤波器规范 {"type",spec} 可以是以下任何形式之一：
-
{"Lowpass",{ωp,ωs},{ap,as}} 使用带通和带阻频率和衰减量的低通滤波器 
{"Highpass",{ωs,ωp},{as,ap}} 高通滤波器 
{"Bandpass",{ωs1,ωp1,ωp2,ωs2},{as,ap}} 带通滤波器 
{"Bandstop",{ωp1,ωs1,ωs2,ωp2},{ap,as}} 带阻滤波器 - 频率数值应该以升序给出.
- 数值 ap 和 as 分别是通带和阻带衰减的绝对值.
- 给出增益分数
，衰减 
.
范例
打开所有单元 关闭所有单元基本范例 (2)
tf = EllipticFilterModel[3]//Chop
tf = EllipticFilterModel[3, s]//ChopBodePlot[tf, GridLines -> Automatic, PlotLayout -> "Magnitude"]tf = EllipticFilterModel[{"Lowpass", {1., 2.}, {1., 20.}}, s]Plot[Abs[tf[I * ω]], {ω, 0, 3}, PlotRange -> All, Epilog -> {Pink, Dashed, Line[{{0, 0.89}, {1, 0.89}, {1, 0.1}}], Line[{{2., 0.89}, {2., 0.1}, {3., 0.1}}]}]范围 (5)
EllipticFilterModel[{2, ω}, s]//N//ChopEllipticFilterModel[{2, 1}, s]EllipticFilterModel[{2, N[1, 24]}, s]BodePlot[EllipticFilterModel[{2, 10.}], GridLines -> Automatic, PlotLayout -> "Magnitude"]BodePlot[EllipticFilterModel[{"Highpass", {1., 10.}, {20., 1.}}], {.1, 100}, GridLines -> Automatic, PlotLayout -> "Magnitude"]tf = EllipticFilterModel[{"Bandpass", {0.1, 1., 10., 100.}, {20, 1}}];
BodePlot[tf, {0.1, 100}, GridLines -> Automatic, PlotLayout -> "Magnitude"]tf = EllipticFilterModel[{"Bandstop", {0.1, 1., 10., 100.}, {1, 20}}];
BodePlot[tf, {0.1, 100}, GridLines -> Automatic, PlotLayout -> "Magnitude"]应用 (5)
tf = EllipticFilterModel[{"Lowpass", {1., 2.}, {1, 40}}];ω = 1 / 5;input = (Sin[ω t] + 1 / 2 Sin[25ω t]) UnitStep[t];
response1 = OutputResponse[tf, input, {t, 0, 100}];椭圆滤波器把响应移动 Arg[tf[ω ]]，其中 ω 是输入正弦波的频率：
Plot[{input, response1}, {t, 20, 100}]delay = Arg[tf[I ω]] / ω//First//First;
Plot[Evaluate[Flatten[{input, response1 /. t -> (t - delay)}]], {t, 20, 100}]tf2 = TransferFunctionTransform[1 / #&, tf];Plot[Evaluate[Flatten[{input, OutputResponse[tf2, input, {t, 0, 100}]}]], {t, 20, 100}]使用满足以下通带和阻带频率和衰减的椭圆近似设计数字低通滤波器：
Subscript[ω, p] = 0.4 π;Subscript[ω, s] = 0.6π;
Subscript[a, p] = 1;Subscript[a, s] = 20;{Subscript[Ω, p] = 2 Tan[(0.4π/2)], Subscript[Ω, s] = 2 Tan[(0.6π/2)]}tf = EllipticFilterModel[{"Lowpass", {Subscript[Ω, p], Subscript[Ω, s]}, {Subscript[a, p], Subscript[a, s]}}, s]dtf = ToDiscreteTimeModel[tf, 1, z]//ChopBodePlot[dtf, {0.1 π, π}, PlotLayout -> "Magnitude", GridLines -> {{Subscript[ω, p], Subscript[ω, s]}, {10^-Subscript[a, p] / 20, 10^-Subscript[a, s] / 20}}, ScalingFunctions -> {"Linear", "Absolute"}, PlotRange -> All]创建长度为 31 的离散时间椭圆 IIR 滤波器的 FIR 近似：
OutputResponse[dtf, KroneckerDelta[n], {n, 0, 30}]//ChopListPlot[%, PlotRange -> All, Filling -> 0]data = Transpose[FinancialData["GE", {"Jan. 1, 2012", "Jan. 1, 2013"}]["Path"]];
fir = OutputResponse[ToDiscreteTimeModel[EllipticFilterModel[{3, 0.66}], 1], KroneckerDelta[n], {n, 0, 100}]//Chop//Flatten;
DateListPlot[{Transpose[data], Transpose[{data[[1]], -ListConvolve[fir, data[[2]], 4]}]}, PlotRange -> All, PlotLegends -> {"original", "smoothed"}]h = ToDiscreteTimeModel[EllipticFilterModel[{"Lowpass", {1., 2.}, {1., 20.}}], 1];
RecurrenceFilter[h, [image]]h = ToDiscreteTimeModel[EllipticFilterModel[{"Highpass", {.5, 1.}, {20., 1.}}], 1];
RecurrenceFilter[h, [image]]属性和关系 (3)
SystemsModelOrder[StateSpaceModel[EllipticFilterModel[{"Highpass", {1, 1.2}, {20, 3}}]]]tf = EllipticFilterModel[7];TransferFunctionPoles[tf]//ChopTransferFunctionZeros[tf]//Choplo = EllipticFilterModel[{3, .5}];
hi = TransferFunctionTransform[(1 / #&), lo]//ChopPlot[{Abs[lo[I w]], Abs[hi[I w]]}, {w, 0, 3}, PlotRange -> All]
Wolfram Research (2012)，EllipticFilterModel，Wolfram 语言函数，https://reference.wolfram.com/language/ref/EllipticFilterModel.html.
文本
Wolfram Research (2012)，EllipticFilterModel，Wolfram 语言函数，https://reference.wolfram.com/language/ref/EllipticFilterModel.html.
CMS
Wolfram 语言. 2012. "EllipticFilterModel." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/EllipticFilterModel.html.
APA
Wolfram 语言. (2012). EllipticFilterModel. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/EllipticFilterModel.html 年