BiquadraticFilterModel
BiquadraticFilterModel
BiquadraticFilterModel[{ω,q}]
使用特征频率 ω 和质量因子 q 创建低通双二阶滤波器.
BiquadraticFilterModel[{"type",spec}]
创建指定 {"type",spec} 的滤波器.
BiquadraticFilterModel[{"type",spec},var]
以变量 var 的形式表示模型.
更多信息
- 双二阶滤波器是由两个二次多项式比率定义的二阶滤波器. 它们是模拟和数字信号处理中最常用的电路.
- BiquadraticFilterModel 返回作为 TransferFunctionModel 的滤波器.
- 滤波器规范 {"type",spec} 可以是以下任何形式：
-
{"Lowpass",{{ω,q}}} 使用截止频率 ω 和质量因子 q 
{"Highpass",{{ω,q}}} 使用截止频率 ω 和质量因子 q 
{"Allpass",{{ω,q}}} 使用频率 ω 和质量因子 q 
{"Bandpass",{ω1,ω2}} 使用角频率 ω1 和 ω2 
{"Bandpass",{{ω,q}}} 使用中心频率 ω 和质量因子 q 
{"Bandstop",{ω1,ω2}} 使用角频率 ω1 和 ω2 
{"Bandstop",{{ω,q}}} 使用中心频率 ω 和质量因子 q - 可以给出下列滤波器规范来创建均衡器：
-
{"Peaking",{{ω,q}},g} 使用增益值 g 的峰值均衡器 
{"LowShelf",{{ω,q}},g} 使用增益值 g 的低通搁置均衡器 
{"HighShelf",{{ω,q}},g} 使用增益值 g 的高通搁置均衡器 - 已知增益值
，衰减量为 
.
范例
打开所有单元 关闭所有单元基本范例 (3)
tf = BiquadraticFilterModel[{1, 1}]BodePlot[tf, GridLines -> Automatic, PlotLayout -> "Magnitude"]tf = BiquadraticFilterModel[{"Bandpass", {{1, 1}}}]BodePlot[tf, {0.1, 10}, GridLines -> Automatic, PlotLayout -> "Magnitude"]in = Sin[ 1 / 5 t] + Sin[5t];
out = OutputResponse[BiquadraticFilterModel[{1, 1}], in, {t, 0, 60}];
Plot[{in, out}, {t, 0, 40}, PlotLegends -> {"Input", "Output"}]范围 (8)
BiquadraticFilterModel[{ω, Q}]BiquadraticFilterModel[{"Lowpass", {{1, 1}}}, s]
tf = BiquadraticFilterModel[{"Lowpass", {{10, 1}}}, s]BodePlot[tf, {1, 100}, GridLines -> Automatic, PlotLayout -> "Magnitude"]
BiquadraticFilterModel[{"Highpass", {{ω, Q}}}]
tf = BiquadraticFilterModel[{"Highpass", {{10, 1}}}, s]BodePlot[tf, {1, 100}, GridLines -> Automatic, PlotLayout -> "Magnitude"]
BiquadraticFilterModel[{"Bandpass", {{ω, Q}}}]
tf = BiquadraticFilterModel[{"Bandpass", {{1, 10}}}, s]BodePlot[tf, {0.1, 10}, GridLines -> Automatic, PlotLayout -> "Magnitude"]
BiquadraticFilterModel[{"Bandstop", {{ω, Q}}}]
tf = BiquadraticFilterModel[{"Bandstop", {{1, 2}}}, s]BodePlot[tf, {0.1, 10}, PlotRange -> {0, -10}, GridLines -> Automatic, PlotLayout -> "Magnitude"]
BiquadraticFilterModel[{"Allpass", {{ω, Q}}}]
tf = BiquadraticFilterModel[{"Allpass", {{1, 2}}}, s]BodePlot[tf, {0.1, 10}, PlotRange -> {5, -15}, GridLines -> Automatic, PlotLayout -> "Magnitude"]符号式 "Peaking" 全通滤波器，其中中心频率为 
，质量因子为 
，增益值为 
：
BiquadraticFilterModel[{"Peaking", {{ω, Q}}, g}]
tf = BiquadraticFilterModel[{"Peaking", {{1, 1}}, Quantity[10, "dB"]}, s]BodePlot[tf, {0.1, 10}, PlotRange -> {-5, 15}, GridLines -> Automatic, PlotLayout -> "Magnitude"]符号式 "LowShelf" 滤波器，其中中心频率为 
，质量因子为 
，增益值为 
：
BiquadraticFilterModel[{"LowShelf", {{ω, Q}}, g}]
tf = BiquadraticFilterModel[{"LowShelf", {{1, 1}}, Quantity[-5, "dB"]}, s]BodePlot[tf, {0.1, 10}, PlotRange -> {-10, 10}, GridLines -> Automatic, PlotLayout -> "Magnitude"]符号式 "HighShelf" 滤波器，其中中心频率为 
，质量因子为 
，增益值为 
：
BiquadraticFilterModel[{"HighShelf", {{ω, Q}}, g}]
tf = BiquadraticFilterModel[{"HighShelf", {{1, 1}}, Quantity[-5, "dB"]}, s]BodePlot[tf, {0.1, 10}, PlotRange -> {-10, 10}, GridLines -> Automatic, PlotLayout -> "Magnitude"]推广和延伸 (1)
tf = BiquadraticFilterModel[{"Lowpass", {{1, 1}}}];
tfs = NestList[SystemsModelSeriesConnect[tf, #]&, tf, 2]BodePlot[tfs, {0.1, 10}, PlotRange -> {20, -120}, GridLines -> Automatic, PlotLayout -> "Magnitude", FrameTicks -> {{Range[0, -120, -40], None}, {Automatic, Automatic}}, PlotLegends -> {"40 dB/decade", "80 dB/decade", "120 dB/decade"}]应用 (1)
in = (Sin[ 1 / 5 t] + Sin[5t]) UnitStep[t];
Plot[in, {t, 20, 60}]tf = BiquadraticFilterModel[{"Lowpass", {{1, 1}}}];
out = OutputResponse[tf, in, {t, 0, 60}];
Plot[out, {t, 20, 60}]tf2 = Nest[SystemsModelSeriesConnect[tf, #]&, tf, 2]out = OutputResponse[tf2, in, {t, 0, 60}];
Plot[out, {t, 20, 60}]属性和关系 (7)
type = {"Lowpass", "Highpass", "Bandpass", "Bandstop"};
tfs = BiquadraticFilterModel[{#, {{1, 1}}}]& /@ type;
BodePlot[tfs, {0.1, 10.}, PlotLayout -> "Phase", GridLines -> Automatic, PlotLegends -> type]提取 BiquadraticFilterModel 的阶数：
SystemsModelOrder[StateSpaceModel[BiquadraticFilterModel[{"Lowpass", {{1., 1.}}}]]]tf = BiquadraticFilterModel[{"Lowpass", {{1, 1}}}];
BodePlot[tf, {0.1, 10}, GridLines -> Automatic, PlotLayout -> "Magnitude"]
tf = BiquadraticFilterModel[{"Lowpass", {{1, #}}}]& /@ {1 / 2, 1, 3, 9};
BodePlot[tf, {0.1, 10}, GridLines -> Automatic, PlotRange -> {-20, 20}, PlotLayout -> "Magnitude", PlotLegends -> {0.5, 1., 3., 9.}]
tf = BiquadraticFilterModel[{"Bandpass", {{1., #}}}]& /@ {0.5, 1., 3.};
BodePlot[tf, {0.1, 10}, GridLines -> Automatic, PlotLayout -> "Magnitude", PlotRange -> {5, -40}, PlotLegends -> {0.5, 1., 3.}]
tfboost = BiquadraticFilterModel[{"Peaking", {{1, 1}}, #}, s]& /@ {4 / 3, 5 / 3, 6 / 3}BodePlot[tfboost, {0.1, 10}, PlotRange -> {-15, 15}, PlotLayout -> "Magnitude", GridLines -> Automatic, PlotLegends -> N@{4 / 3, 5 / 3, 6 / 3}]
tfcut = BiquadraticFilterModel[{"Peaking", {{1, 1}}, #}, s]& /@ {3 / 6, 3 / 5, 3 / 4}BodePlot[tfcut, {0.1, 10}, PlotRange -> {-15, 15}, PlotLayout -> "Magnitude", GridLines -> Automatic, PlotLegends -> N@{3 / 6, 3 / 5, 3 / 4}]
tfboost = BiquadraticFilterModel[{"LowShelf", {{1, 1}}, #}, s]& /@ {4 / 3, 5 / 3, 6 / 3}BodePlot[tfboost, {0.1, 10}, PlotRange -> {-15, 15}, PlotLayout -> "Magnitude", GridLines -> Automatic, PlotLegends -> N@{4 / 3, 5 / 3, 6 / 3}]
tfcut = BiquadraticFilterModel[{"LowShelf", {{1, 1}}, #}, s]& /@ {3 / 6, 3 / 5, 3 / 4}BodePlot[tfcut, {0.1, 10}, PlotRange -> {-15, 15}, PlotLayout -> "Magnitude", GridLines -> Automatic, PlotLegends -> N@{3 / 6, 3 / 5, 3 / 4}]
Wolfram Research (2016)，BiquadraticFilterModel，Wolfram 语言函数，https://reference.wolfram.com/language/ref/BiquadraticFilterModel.html.
文本
Wolfram Research (2016)，BiquadraticFilterModel，Wolfram 语言函数，https://reference.wolfram.com/language/ref/BiquadraticFilterModel.html.
CMS
Wolfram 语言. 2016. "BiquadraticFilterModel." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/BiquadraticFilterModel.html.
APA
Wolfram 语言. (2016). BiquadraticFilterModel. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/BiquadraticFilterModel.html 年