WhiteNoiseProcess
WhiteNoiseProcess
表示高斯（Gaussian）白噪声过程，其中均值为0，标准偏差为1.
表示高斯（Gaussian）白噪声过程，其中均值为0，标准偏差为 σ.
WhiteNoiseProcess[dist]
表示基于分布 dist 的白噪声过程.
更多信息
- WhiteNoiseProcess 也称为独立同分布（iid）过程.
- WhiteNoiseProcess 是一个离散随机过程.
- WhiteNoiseProcess 的成份（slice）被假设为独立同分布的随机变量.
- 分布 dist 可以是任何均值为0，具有有限方差的单变量分布.
- WhiteNoiseProcess 可与函数 Mean、PDF、Probability 和 RandomFunction 一起使用.
范例
打开所有单元 关闭所有单元基本范例 (1)
𝒫 = WhiteNoiseProcess[];data = RandomFunction[𝒫, {0, 40}];ListPlot[RandomFunction[𝒫, {0, 40}], Filling -> Axis]{Mean[𝒫[t]], Variance[𝒫[t]]}CovarianceFunction[𝒫, s, t]范围 (2)
𝒫 = WhiteNoiseProcess[5];data = RandomFunction[𝒫, {0, 30}];ListPlot[data, Filling -> Axis]𝒫 = WhiteNoiseProcess[UniformDistribution[{-1, 1}]];data = RandomFunction[𝒫, {0, 30}];ListPlot[data, Filling -> Axis]𝒫 = WhiteNoiseProcess[DiscreteUniformDistribution[{-1, 1}]];data = RandomFunction[𝒫, {0, 30}];ListPlot[data, Filling -> Axis]𝒫 = WhiteNoiseProcess[MixtureDistribution[{0.6, 0.4}, {NormalDistribution[], NormalDistribution[0, 3]}]];sample = RandomFunction[𝒫, {0, 100}, 2];ListPlot[sample, Filling -> Axis]EstimatedProcess[sample, WhiteNoiseProcess[MixtureDistribution[{a, b}, {NormalDistribution[], NormalDistribution[0, 3]}]]]应用 (2)
𝒫 = TransformedProcess[Cos[t / 8] + noise[t], noiseWhiteNoiseProcess[UniformDistribution[{-1 / 5, 1 / 5}]], t];data = RandomFunction[𝒫, {0, 200}];ListPlot[data, Filling -> Axis]𝒫 = TransformedProcess[x[t] + 2 x[t - 1] + 7x[t - 2], xWhiteNoiseProcess[], t];data = RandomFunction[𝒫, {2, 50}, 3];ListLinePlot[data, PlotRange -> All]{Mean[𝒫[t]], Variance[𝒫[t]], Kurtosis[𝒫[t]]}比较对应的 MAProcess 的特征值：
𝒫1 = MAProcess[{2, 7}, 1];{Mean[𝒫1[t]], Variance[𝒫1[t]], Kurtosis[𝒫1[t]]}属性和关系 (6)
WhiteNoiseProcess 是一个离散过程：
ProcessTimeDomain[WhiteNoiseProcess[]]ProcessStateDomain[WhiteNoiseProcess[UniformDistribution[{-1, 1}]]]ProcessStateDomain[WhiteNoiseProcess[DiscreteUniformDistribution[{-1, 1}]]]SliceDistribution[WhiteNoiseProcess[dist],t] 等价于 dist：
dist = NormalDistribution[0, 5];𝒫 = WhiteNoiseProcess[dist];𝒫[t]𝒫[{s, t}]Mean[WhiteNoiseProcess[][t]]Mean[WhiteNoiseProcess[UniformDistribution[{-a, a}]][t]]根据 AutocorrelationTest，WhiteNoiseProcess 是不相关的：
data = RandomFunction[WhiteNoiseProcess[], {0, 10 ^ 5}];AutocorrelationTest[data, 1, "TestConclusion"]高斯白噪声是 MAProcess 的特殊情况：
Mean[#[t]]& /@ {MAProcess[{}, σ ^ 2], WhiteNoiseProcess[NormalDistribution[0, σ]]}CovarianceFunction[MAProcess[{}, σ ^ 2], h]CovarianceFunction[WhiteNoiseProcess[NormalDistribution[0, σ]], h]% - %%//Simplify可能存在的问题 (1)
对于包含来自于均匀分布的白噪声的例子，EstimatedProcess 不工作：
sample = RandomFunction[WhiteNoiseProcess[UniformDistribution[{-2, 2}]], {1, 10}];EstimatedProcess[sample, WhiteNoiseProcess[UniformDistribution[{a, b}]]]
对 UniformDistribution 使用对称区间，对该情况起到帮助：
EstimatedProcess[sample, WhiteNoiseProcess[UniformDistribution[{-a, a}]]]巧妙范例 (1)
𝒫1 = WhiteNoiseProcess[];
𝒫2 = WhiteNoiseProcess[3];
𝒫3 = WhiteNoiseProcess[UniformDistribution[{-2, 2}]];
𝒫4 = WhiteNoiseProcess[DiscreteUniformDistribution[{-2, 2}]];
𝒫5 = WhiteNoiseProcess[MixtureDistribution[{3, 7}, {UniformDistribution[{-3, 3}], UniformDistribution[{-1, 1}]}]];
𝒫6 = WhiteNoiseProcess[MixtureDistribution[{2, 3}, {NormalDistribution[], NormalDistribution[0, 4]}]];data = RandomFunction[#, {0, 50}]& /@ {𝒫1, 𝒫2, 𝒫3, 𝒫4, 𝒫5, 𝒫6};Table[ListPlot[data[[i]], Filling -> Axis, PlotLabel -> StringJoin["𝒫", ToString[i]]], {i, 6}]
Wolfram Research (2014)，WhiteNoiseProcess，Wolfram 语言函数，https://reference.wolfram.com/language/ref/WhiteNoiseProcess.html.
文本
Wolfram Research (2014)，WhiteNoiseProcess，Wolfram 语言函数，https://reference.wolfram.com/language/ref/WhiteNoiseProcess.html.
CMS
Wolfram 语言. 2014. "WhiteNoiseProcess." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/WhiteNoiseProcess.html.
APA
Wolfram 语言. (2014). WhiteNoiseProcess. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/WhiteNoiseProcess.html 年