ContinuousWaveletData[{{oct1,voc1}coef1,…},wave]
产生一个连续小波数据对象,其中小波系数为对应于倍频程与音频 {octi,voci} 的 coefi,小波为 wave.
ContinuousWaveletData
ContinuousWaveletData[{{oct1,voc1}coef1,…},wave]
产生一个连续小波数据对象,其中小波系数为对应于倍频程与音频 {octi,voci} 的 coefi,小波为 wave.
更多信息和选项
- ContinuousWaveletData[{{oct1,voc1}->coef1,…},…] 恒能转换为结构为 ContinuousWaveletData[coefs,octvocs,…] 的最佳标准形式.
- 系数 coefi 可以为向量、 Sound[…] 或 SampledSoundList[…]对象.
- ContinuousWaveletTransform 所用的选项也可用作 ContinuousWaveletData 的选项.
- 在标准输出形式中,仅打印原始数据的倍频程数、音频数与维数.
- Normal[ContinuousWaveletData[…]] 给出规则列表 {{oct1,voc1}->coef1,{oct2,voc2}->coef2,…},该规则列表给出每一对倍频程与音频 {octi,voci} 和对应的系数数组 coefi 的对应关系.
- ContinuousWaveletData 表示多重尺度
上的连续小波变换
. - 各尺度
由一个倍频程数
与音频数
指定,并由
得到. - 尺度 {oct,voc} 可用于从 ContinuousWaveletData 对象 cwd 中提取小波系数. 可以给出下列指定:
-
cwd[{oct,voc}] 提取对应于 {oct,voc} 的系数 cwd[{{oct1,voc1},{oct2,voc2},…}] 提取多个小波系数数组 cwd[ovpatt] 提取尺度匹配 ovpatt 的全部系数 cwd[All] 提取全部系数 - 缺省时,系数以规则列表 {{oct1,voc1}->coef1,{oct2,voc2}->coef2,…} 的形式返回.
- cwd[…,{form1,form2,…}] 可用于控制输出形式. 可能的形式 formi 包括:
-
"Rules" 规则 {{oct1,voc1}->…} "Values" 仅系数 "Inverse" 个别系数的逆变换 "ListPlot" 1D 系数的简单列表图形 "Sound" 声音系数的声音对象 "SampledSoundList" 声音系数的取样声音对象 - 小波表示的属性由 ContinuousWaveletData[…]["prop"] 得到.
- ContinuousWaveletData[…]["Properties"] 给出 ContinuousWaveletData 对象可用的属性列表.
- 与变换系数相关的属性包括:
-
"Octaves" 所用的倍频程数 "Voices" 每个倍频程所用的音频数 "Scales" 所用的小波尺度 "Wavelet" 所用的小波族 "WaveletScale" 最小的可解尺度 "WaveletIndex" 全部小波索引{octi,voci}的列表 "LogScalogramFunction" 给出函数 
"LinearScalogramFunction" 给出函数 
- 与输入数据相关的属性包括:
-
"DataDimensions" 原始数据的维数 "DataChannels" 数据的频道数 "DataMean" 原始数据的均值 "DataWrapper" 在重构后应用于数据的封装函数 "SampleRate" 用于输入数据的样本率
范例
打开所有单元 关闭所有单元基本范例 (2)
得到 ContinuousWaveletData 对象:
cwd = ContinuousWaveletTransform[Sin[Range[40] / 5]]ContinuousWaveletData 表示不同尺度 {oct,voc} 上的系数数组:
WaveletScalogram[cwd, Ticks -> Full]提取包括对应于各 {oct,voc} 的数值尺度在内的属性:
cwd["Scales"]InverseContinuousWaveletTransform[ContinuousWaveletData[{{2, 1} -> {1, 0, 3, 3, 0, 2}, {3, 2} -> {-2, 2.5, 1, 1, 0, 0}}, PaulWavelet[]]]范围 (12)
基本用途 (10)
由 ContinuousWaveletTransform 得到一个 ContinuousWaveletData 对象:
cwd = ContinuousWaveletTransform[{1, 2, 3, 4}]cwd["WaveletIndex"]Normal[cwd]InverseContinuousWaveletTransform 在 ContinuousWaveletData 上运算:
data = AiryAi[-Range[100] / 10];cwd = ContinuousWaveletTransform[data, Automatic, {8, 8}]{ListLinePlot[data, PlotLabel -> "original"], ListLinePlot[InverseContinuousWaveletTransform[cwd], PlotLabel -> "reconstructed"]}cwd = ContinuousWaveletTransform[{1, 1, 3, 1}, Automatic, {3, 2}]cwd[{{1, 1}}]cwd[{1, _}]cwd[{{1, 1}, {3, 2}, {2, _}}]cwd = ContinuousWaveletTransform[{1, 1, 3, 1}, Automatic, {3, 2}]cwd[{{1, 1}, {2, 2}}, "Rules"]cwd[{{1, 1}, {2, 2}}, "Values"]cwd[{{1, 1}, {2, 2}}, "ListPlot"]cwd[{{1, 1}, {2, 2}}, "Inverse"]cwd[{{1, 1}, {2, 2}}, {"Values", "ListPlot"}]得到作为 Sound 对象的声音小波系数:
cwd = ContinuousWaveletTransform[ExampleData[{"Sound", "Tuba"}]]cwd[{3, 2}, "Sound"]cwd = ContinuousWaveletTransform[RandomReal[1, 12], MorletWavelet[]]{cwd["Octaves"], cwd["Voices"], cwd["Wavelet"]}cwd["Properties"]在其它小波函数中使用 ContinuousWaveletData:
data = Table[Sin[x + x^2], {x, 0, 10, 0.1}];cwd = ContinuousWaveletTransform[data]InverseContinuousWaveletTransform[cwd]//ListLinePlotWaveletScalogram[cwd]data = Table[Sin[20Log[x]], {x, 1, 10, 0.1}];cwd1 = ContinuousWaveletTransform[data, Automatic, 3]cwd2 = WaveletMapIndexed[c Rescale[c, {0, 1 + I}], cwd1]cwd3 = WaveletMapIndexed[c 0c, cwd1, {2, _}]Table[WaveletScalogram[cwd], {cwd, {cwd1, cwd2, cwd3}}]由一个给出系数数组的规则列表构造 ContinuousWaveletData:
cwd = ContinuousWaveletData[{{1, 1} -> {-1, 1, 1, 1}, {2, 3} -> {2, 3, 3, 0}}]cwd["WaveletIndex"]Normal[cwd]构造一个使用指定小波的 ContinuousWaveletData:
cwd = ContinuousWaveletData[{{1, 1} -> {-1, 1, 1, 1}, {2, 3} -> {2, 3, 3, 0}}, PaulWavelet[]]InverseContinuousWaveletTransform[cwd]属性 (2)
cwd = ContinuousWaveletTransform[RandomReal[1, 8], MexicanHatWavelet[]]{cwd["Wavelet"], cwd["WaveletScale"]}{cwd["Octaves"], cwd["Voices"]}cwd["WaveletIndex"]cwd["Scales"]data = Sound[«1»];cwd = ContinuousWaveletTransform[data]{cwd["DataDimensions"], cwd["DataChannels"], cwd["SampleRate"]}cwd["DataWrapper"]{Head[data], Head[InverseContinuousWaveletTransform[cwd]]}选项 (5)
SampleRate (1)
对于 Sound 输入,自动计算 SampleRate:
snd = Sound[SampledSoundList[Table[Cos[100 t^2], {t, 0, 1, 1. / 255}], 250]]cwd = ContinuousWaveletTransform[snd]默认情况下,从第一个系数规则提取 SampleRate:
srules = cwd[All, "Sound"];First[srules]InverseContinuousWaveletTransform[ContinuousWaveletData[srules]]显式指定 SampleRate:
InverseContinuousWaveletTransform[ContinuousWaveletData[srules, SampleRate -> 150]]WaveletScale (2)
默认情况下,自动计算 WaveletScale:
data = Table[Sin[x^2], {x, 0, 3 π, (3 π/1023)}];ListLinePlot[data]cwt1 = ContinuousWaveletTransform[data, GaborWavelet[6]]cwt2 = ContinuousWaveletData[Normal[cwt1], GaborWavelet[6]]cwt1["WaveletScale"] == cwt2["WaveletScale"]显式设置 WaveletScale:
cwd = ContinuousWaveletData[{{1, 1} -> {1, 2, 3, 4}, {2, 1} -> {1, 2, 3, 4}}, GaborWavelet[6], WaveletScale -> 1]cwd["WaveletScale"]WorkingPrecision (2)
默认情况下,使用 WorkingPrecision->MachinePrecision:
cwd1 = ContinuousWaveletData[{{1, 1} -> {1, 2, 3, 4}, {2, 1} -> {1, 2, 3, 4}}]cwd2 = ContinuousWaveletData[{{1, 1} -> {1, 2, 3, 4}, {2, 1} -> {1, 2, 3, 4}}, WorkingPrecision -> MachinePrecision]cwd1 == cwd2cwd = Normal@ContinuousWaveletData[{{1, 1} -> {0, 1, Sqrt[2], Sqrt[3], 4}, {2, 1} -> {0, 1, Sqrt[2], Sqrt[3], 4}}, WorkingPrecision -> 25]{Precision[cwd], Accuracy[cwd]}属性和关系 (5)
cwd = ContinuousWaveletTransform[Range[8]]Map[Length, cwd[All, "Values"]]ContinuousWaveletData 表示在一组尺度上的连续变换系数:
cwd = ContinuousWaveletTransform[{1, 1, 8, 1, 1, 2, 2, 1, 1}]{TableForm[cwd["Scales"]], WaveletScalogram[cwd, Ticks -> Full]}DiscreteWaveletData 表示一个离散变换系数的树结构:
dwd = DiscreteWaveletTransform[{1, 1, 8, 1, 1, 2, 2, 1, 1}]{dwd["TreeView"], WaveletListPlot[dwd, Ticks -> Full, PlotLayout -> "CommonYAxis"]}从系数和属性重建一个 ContinuousWaveletData:
cwd = ContinuousWaveletTransform[Range[-2, 2], MexicanHatWavelet[]]cwd2 = ContinuousWaveletData[Normal[cwd], cwd["Wavelet"], WaveletScale -> cwd["WaveletScale"]]{cwd["DataDimensions"], cwd2["DataDimensions"]}InverseContinuousWaveletTransform[cwd] == InverseContinuousWaveletTransform[cwd2]cwd = ContinuousWaveletTransform[{1, 2, 3, 4}]使用 Normal:
Normal[cwd]显式提取 All 系数:
cwd[All]指定模式 Blank[] (_),匹配任何倍频程与音频:
cwd[_]cwd = ContinuousWaveletTransform[{1, 2, 3, 4}, Automatic, {3, 2}]将 Last 应用于各个由 cwd[{oct,voc}] 返回的规则:
Last /@ cwd[{2, _}]使用 Part:
cwd[{2, _}][[All, 2]]cwd[{2, _}, "Values"]相关指南
-
▪
- 小波分析
文本
Wolfram Research (2010),ContinuousWaveletData,Wolfram 语言函数,https://reference.wolfram.com/language/ref/ContinuousWaveletData.html.
CMS
Wolfram 语言. 2010. "ContinuousWaveletData." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/ContinuousWaveletData.html.
APA
Wolfram 语言. (2010). ContinuousWaveletData. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/ContinuousWaveletData.html 年
BibTeX
@misc{reference.wolfram_2026_continuouswaveletdata, author="Wolfram Research", title="{ContinuousWaveletData}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/ContinuousWaveletData.html}", note=[Accessed: 13-September-2026]}
BibLaTeX
@online{reference.wolfram_2026_continuouswaveletdata, organization={Wolfram Research}, title={ContinuousWaveletData}, year={2010}, url={https://reference.wolfram.com/language/ref/ContinuousWaveletData.html}, note=[Accessed: 13-September-2026]}