WaveletScalogram[wd]
绘制 DiscreteWaveletData 或 ContinuousWaveletData 对象 wd 的小波向量系数.
WaveletScalogram[wd,wind]
绘制对应于小波索引指标 wind 的小波系数.
WaveletScalogram[wd,wind,func]
绘制前,应用 func 于系数.
WaveletScalogram
WaveletScalogram[wd]
绘制 DiscreteWaveletData 或 ContinuousWaveletData 对象 wd 的小波向量系数.
WaveletScalogram[wd,wind]
绘制对应于小波索引指标 wind 的小波系数.
WaveletScalogram[wd,wind,func]
绘制前,应用 func 于系数.
更多信息和选项
- WaveletScalogram 把变换系数作为着色矩形的行来绘制,其中越大的绝对值显示越深,其后每行对应于不同的小波索引指标.
- 小波索引指标 wind 与 DiscreteWaveletData 或 ContinuousWaveletData 中使用的相同.
- WaveletScalogram[wd] 等同于 WaveletScalogram[wd,Automatic].
- 以下特殊值可用于 func:
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"AbsoluteGlobal" 绝对值除以最大系数 "AbsoluteLevel" 绝对值除以最大级系数 - WaveletScalogram 具有与 Graphics 同样的选项,有以下变化: [所有选项的列表]
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ColorFunction Automatic 如何着色小波系数 ColorFunctionScaling True 是否缩放 ColorFunction 的参数 - WaveletScalogram 返回一个 Graphics 对象.
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AlignmentPoint Center 在图形内对齐的缺省点 AspectRatio Automatic 高与宽的比 Axes False 是否绘制轴 AxesLabel None 坐标轴标签 AxesOrigin Automatic 坐标轴原点 AxesStyle {} 坐标轴样式指定 Background None 绘图的背景色 BaselinePosition Automatic 如何与环绕文本基线对齐 BaseStyle {} 图形的基本样式指定 ColorFunction Automatic 如何着色小波系数 ColorFunctionScaling True 是否缩放 ColorFunction 的参数 ContentSelectable Automatic 是否允许进行内容选择 CoordinatesToolOptions Automatic 坐标工具的详细行为 Epilog {} 主图形之后执行的图形指令 FormatType TraditionalForm 文本的缺省样式类型 Frame False 是否在图形周围放置边框 FrameLabel None 边框标签 FrameStyle {} 边框的样式指定 FrameTicks Automatic 边框刻度 FrameTicksStyle {} 边框刻度的样式指定 GridLines None 绘制的网格线 GridLinesStyle {} 网格线的样式指定 ImageMargins 0. 图形周围的边幅 ImagePadding All 为标签等额外填充内容 ImageSize Automatic 图形的绝对尺寸 LabelStyle {} 标签的样式指定 Method Automatic 使用图形方式的细节 PlotLabel None 图形的一个整体标签 PlotRange All 图形值的范围 PlotRangeClipping False 是否在图形范围剪切 PlotRangePadding Automatic 填充图形值范围的程度 PlotRegion Automatic 填充的最后显示区域 PreserveImageOptions Automatic 当显示相同图形的新版本时,是否保存图形选项 Prolog {} 主图形之前执行的图形指令 RotateLabel True 是否在边框上旋转 y 标签 Ticks Automatic 坐标轴标记 TicksStyle {} 坐标轴标记的样式指定
所有选项的列表
范例
打开所有单元 关闭所有单元基本范例 (2)
DiscreteWaveletTransform[Table[Sin[x^2], {x, -6, 6, 0.01}], Automatic, 8];WaveletScalogram[%]ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]];WaveletScalogram[%]范围 (10)
DiscreteWaveletData (6)
data = Table[Sin[20x] + Sin[10x], {x, 1, 10, 0.01}];ListLinePlot[data]dwd = DiscreteWaveletTransform[data, Automatic, 4];WaveletScalogram[dwd]使用 Full 刻度扩展垂直轴上的标记:
WaveletScalogram[dwd, Ticks -> Full]dwd = DiscreteWaveletTransform[Table[Sin[20x] + Sin[10x], {x, 1, 10, 0.01}], Automatic, 4];dwd["TreeView"]WaveletScalogram[dwd, {___, 1}, Ticks -> Full]dwd = DiscreteWaveletTransform[Table[Sin[20x] + Sin[10x], {x, 1, 10, 0.01}], Automatic, 4];WaveletScalogram[dwd, Automatic, Abs[Log[#]^2]&]data = Table[n ^ 4 (-1) ^ (100 n) + Sqrt[1 - n], {n, 0, 1, 0.01}];ListLinePlot[data]dwd = DiscreteWaveletTransform[data, Automatic, 3, Padding -> 0];WaveletScalogram[dwd, AxesLabel -> {"time", "scale"}]使用 WaveletListPlot 使尺度谱图更完美:
data = Table[Sin[x ^ 3], {x, 0, 10, 0.02}];ListLinePlot[data]dwd = DiscreteWaveletTransform[data, DaubechiesWavelet[3], 3];WaveletScalogram[dwd, ColorFunction -> "BlueGreenYellow"]尺度谱图中的颜色变化用 WaveletListPlot 更直观:
WaveletListPlot[dwd, ColorFunction -> "BlueGreenYellow", Filling -> Axis]WaveletScalogram 可用于任何变换产生的 DiscreteWaveletData:
f[t_] := (4/1 + Exp[-6.4t + 3.2]) + Cos[100 π t]Piecewise[{{1, t ≥ (1/3) && t ≤ (2/3)}}, 0]data = Table[f[t], {t, 0, 1, 0.001}];ListLinePlot[data]绘制 DiscreteWaveletTransform 和 DiscreteWaveletPacketTransform 的尺度谱图:
Table[WaveletScalogram[wt[data], {___, 1}, ColorFunction -> "RustTones", PlotLabel -> wt], {wt, {DiscreteWaveletTransform, DiscreteWaveletPacketTransform}}]绘制 StationaryWaveletTransform 和StationaryWaveletPacketTransform 的尺度谱图:
Table[WaveletScalogram[wt[data], {___, 1}, ColorFunction -> "RustTones", PlotLabel -> wt], {wt, {StationaryWaveletTransform, StationaryWaveletPacketTransform}}]ContinuousWaveletData (4)
data = Table[Sin[20x] + Sin[10x], {x, 1, 10, 0.01}];ListLinePlot[data]cwd = ContinuousWaveletTransform[data, Automatic];WaveletScalogram[cwd]使用 Full 刻度扩展垂直轴的标记:
WaveletScalogram[cwd, Ticks -> Full]cwd = ContinuousWaveletTransform[Table[Sin[20x] + Sin[10x], {x, 1, 10, 0.01}]];WaveletScalogram[cwd, {4 | 5 | 6 | 7, _}]cwd = ContinuousWaveletTransform[Table[Sin[20x] + Sin[10x], {x, 1, 10, 0.01}]];WaveletScalogram[cwd, Automatic, Abs[Log[#]^2]&]data1 = Table[Cos[20 π x], {x, 0, 1, (1/1023)}];ListLinePlot[data1]cwt1 = ContinuousWaveletTransform[data1, GaborWavelet[6]];WaveletScalogram[cwt1]data2 = Table[Cos[20 π x] + Cos[Sqrt[2]50 π x], {x, 0, 1, (1/1023)}];ListLinePlot[data2]cwt2 = ContinuousWaveletTransform[data2, GaborWavelet[6]];WaveletScalogram[cwt2]选项 (43)
AspectRatio (1)
默认情况下,WaveletScalogram 使用固定的高宽比:
data = ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]];WaveletScalogram[data]通过 AspectRatio1 使高等和宽度相等:
WaveletScalogram[data, AspectRatio -> 1]AspectRatioAutomatic 根据绘图范围确定高宽比:
WaveletScalogram[data, AspectRatio -> Automatic]AspectRatioFull 调整高度和宽度以便可以恰当地放在其他结构的里面:
plot = WaveletScalogram[data, AspectRatio -> Full];{Framed[Pane[plot, {50, 100}]], Framed[Pane[plot, {100, 100}]], Framed[Pane[plot, {100, 50}]]}Axes (3)
WaveletScalogram[DiscreteWaveletTransform[Table[Sin[t^2], {t, -3π, 3π, 6π / 1023}]]]WaveletScalogram[DiscreteWaveletTransform[Table[Sin[t^2], {t, -3π, 3π, 6π / 1023}]], Axes -> False]{WaveletScalogram[DiscreteWaveletTransform[Table[Sin[t^2], {t, -3π, 3π, 6π / 1023}]], Axes -> {True, False}], WaveletScalogram[DiscreteWaveletTransform[Table[Sin[t^2], {t, -3π, 3π, 6π / 1023}]], Axes -> {False, True}]}AxesLabel (3)
WaveletScalogram[DiscreteWaveletTransform[Table[Sin[t^2], {t, -3π, 3π, 6π / 1023}]]]WaveletScalogram[DiscreteWaveletTransform[Table[Sin[t^2], {t, -3π, 3π, 6π / 1023}]], AxesLabel -> y]WaveletScalogram[DiscreteWaveletTransform[Table[Sin[t^2], {t, -3π, 3π, 6π / 1023}]], AxesLabel -> {Label1, Label2}]AxesOrigin (2)
AxesOrigin 的 Automatic 设置是 {0,0}:
DiscreteWaveletTransform[Table[Sin[t^4], {t, -3π, 3π, 6π / 1023}]];WaveletScalogram[%, AxesOrigin -> Automatic]DiscreteWaveletTransform[Table[Sin[t^4], {t, -3π, 3π, 6π / 1023}]];WaveletScalogram[%, AxesOrigin -> {0, 7}]AxesStyle (3)
WaveletScalogram[DiscreteWaveletTransform[Table[Sin[t^2], {t, -3π, 3π, 6π / 1023}]], AxesStyle -> Red]WaveletScalogram[DiscreteWaveletTransform[Table[Sin[t^2], {t, -3π, 3π, 6π / 1023}]], AxesStyle -> {{Thick, Red}, {Thick, Blue}}]WaveletScalogram[DiscreteWaveletTransform[Table[Sin[t^2], {t, -3π, 3π, 6π / 1023}]], AxesStyle -> Green, TicksStyle -> Red]ColorFunction (3)
DiscreteWaveletTransform[Table[Sin[t^3], {t, -3π, 3π, 6π / 1023}]];WaveletScalogram[%, ColorFunction -> (Blend[{Orange, Blue}, #]&)]DiscreteWaveletTransform[Table[Sin[t^3], {t, -3π, 3π, 6π / 1023}]];WaveletScalogram[%, ColorFunction -> ColorData[{"DeepSeaColors", "Reversed"}]]DiscreteWaveletTransform[Table[Sin[t^3], {t, -3π, 3π, 6π / 1023}]];WaveletScalogram[%, ColorFunction -> Hue]ColorFunctionScaling (2)
cwd = ContinuousWaveletTransform[Table[Sin[x^2], {x, 0, 3π, 0.01}]];Table[WaveletScalogram[cwd, Automatic, Abs@Log[#]&, ColorFunctionScaling -> cf, PlotLabel -> cf], {cf, {False, True}}]为了更广泛地使用 ColorFunction,设置 ColorFunctionScaling 为 False:
cwd = ContinuousWaveletTransform[Table[Sin[x^2], {x, 0, 3π, 0.01}]];Table[WaveletScalogram[cwd, Automatic, ColorFunctionScaling -> cf, ColorFunction -> "HypsometricTints", PlotLabel -> cf], {cf, {False, True}}]Frame (3)
DiscreteWaveletTransform[Table[t Sinc[t^2], {t, -3π, 3π, 6π / 1023}]];WaveletScalogram[%, Frame -> True]dwt = DiscreteWaveletTransform[ Table[t Sinc[t^2], {t, -3π, 3π, 6π / 1023}]];WaveletScalogram[dwt, Frame -> {{True, True}, {False, False}}]WaveletScalogram[dwt, Frame -> {{False, False}, {True, True}}]DiscreteWaveletTransform[ Table[t Sinc[t^2], {t, -3π, 3π, 0.01}]];WaveletScalogram[%, Frame -> True, FrameStyle -> Directive[Red, 12]]FrameTicks (3)
cwd = ContinuousWaveletTransform[Table[Sin[x^2], {x, 0, 3π, 0.01}]];WaveletScalogram[cwd, Frame -> True, FrameTicks -> All]使用 Full 记号在垂直轴上绘制表明倍频程与音频 {oct,voc} 的标签:
WaveletScalogram[cwd, Frame -> True, FrameTicks -> Full]cwd = ContinuousWaveletTransform[Table[Sin[x^2], {x, 0, 3π, 0.01}]];ticks = {#, Superscript[2, #]}& /@ Range[8];WaveletScalogram[cwd, Frame -> True, FrameTicks -> {{ticks, Automatic}, Automatic}]使用 FrameTicksStyle 指定整个边框刻度样式,包括边框刻度标记:
ContinuousWaveletTransform[Table[Sin[x^2], {x, 0, 3π, 0.01}]];WaveletScalogram[%, Frame -> True, FrameTicksStyle -> Brown]GridLines (3)
ContinuousWaveletTransform[Table[2Cos[160π x]Exp[-50π(x - 0.5)^2], {x, 0, 1, 0.01}]];WaveletScalogram[%, GridLines -> Automatic]ContinuousWaveletTransform[Table[2Cos[160π x]Exp[-50π(x - 0.5)^2], {x, 0, 1, 0.01}]];WaveletScalogram[%, GridLines -> {{40, 60}, {2, 4}}]ContinuousWaveletTransform[Table[2Cos[160π x]Exp[-50π(x - 0.5)^2], {x, 0, 1, 0.01}]];WaveletScalogram[%, GridLines -> Automatic, GridLinesStyle -> Directive[Dashed, Orange]]ImageSize (7)
使用已命名尺寸,如 Tiny、Small、Medium 和 Large:
{WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], ImageSize -> Tiny], WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], ImageSize -> Small]}{WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], ImageSize -> 150], WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], AspectRatio -> 1, ImageSize -> 150]}{WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], ImageSize -> {Automatic, 150}], WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], AspectRatio -> 1, ImageSize -> {Automatic, 150}]}{WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], ImageSize -> UpTo[200]], WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], AspectRatio -> 1, ImageSize -> UpTo[200]]}WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], ImageSize -> {200, 200}, Background -> StandardGray]设置 AspectRatioFull 将填充可用空间:
WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], AspectRatio -> Full, ImageSize -> {200, 200}, Background -> StandardGray]{WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], ImageSize -> {UpTo[150], UpTo[100]}], WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], AspectRatio -> 1, ImageSize -> {UpTo[150], UpTo[100]}]}Framed[Pane[WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], ImageSize -> Full, Background -> StandardGray], {200, 100}]]Framed[Pane[WaveletScalogram[ContinuousWaveletTransform[Table[Sign[Cos[x^2]], {x, -6, 6, 0.05}]], AspectRatio -> Full, ImageSize -> {Scaled[0.5], Scaled[0.5]}, Background -> StandardGray], {200, 200}]]Method (2)
像 MatrixPlot 一样使用非线性光栅函数:
ContinuousWaveletTransform[Table[Sin[x^2], {x, 0, 3π, 0.01}]];Table[WaveletScalogram[%, Method -> {"RasterFunction" -> r}, PlotLabel -> r], {r, {"Raster", "MatrixRaster"}}]反转 DiscreteWaveletData 的小波系数:
DiscreteWaveletTransform[Table[Sin[t^2], {t, 0, 3π, 0.01}]];Table[WaveletScalogram[%, Method -> {"Inverse" -> r}, PlotLabel -> r], {r, {False, True}}]Ticks (4)
WaveletScalogram[DiscreteWaveletTransform[Table[Sin[x ^ 2], {x, -6, 6, 0.01}], Automatic, 8]]WaveletScalogram[DiscreteWaveletTransform[Table[Sin[x ^ 2], {x, -6, 6, 0.01}], Automatic, 8], Ticks -> None]WaveletScalogram[DiscreteWaveletTransform[Table[Sin[x ^ 2], {x, -6, 6, 0.01}], Automatic, 8], Ticks -> {{200, 500, 700, 900}, {8, 6, 4, 2}}]WaveletScalogram[DiscreteWaveletTransform[Table[Sin[x ^ 2], {x, -6, 6, 0.01}], Automatic, 8], Ticks -> {{{200, a}, {500, b}, {700, c}, {900, d}}, {{8, e}, {6, f}, {4, g}, {2, h}}}]TicksStyle (4)
WaveletScalogram[DiscreteWaveletTransform[Table[Sin[x ^ 2], {x, -6, 6, 0.01}], Automatic, 8], TicksStyle -> Directive[Blue, Thick]]WaveletScalogram[DiscreteWaveletTransform[Table[Sin[x ^ 2], {x, -6, 6, 0.01}], Automatic, 8], TicksStyle -> {Directive[Blue, Thick], Directive[Red, Thick]}]WaveletScalogram[DiscreteWaveletTransform[Table[Sin[x ^ 2], {x, -6, 6, 0.01}], Automatic, 8], Ticks -> {{{200, a, .05}, {500, b, .1}, {700, c, .15}, {900, d, .15}}, {{8, e, .1}, {6, f, .2}, {4, g, .3}, {2, h, .25}}}]WaveletScalogram[DiscreteWaveletTransform[Table[Sin[x ^ 2], {x, -6, 6, 0.01}], Automatic, 8], Ticks -> {{{200, a, .05, Directive[Red]}, {500, b, .15, Directive[Green, Thick]}, {700, c, .15, Directive[Blue, Thick]}, {900, d, .15, Directive[Red, Thick]}}, {{8, e, .1, Directive[Blue]}, {6, f, .2, Directive[Blue, Dashed, Thick]}, {4, g, .3, Directive[Dashed, Blue]}, {2, h, .25, Directive[Magenta]}}}]应用 (2)
WaveletScalogram 可用于观看不连续性:
data = Table[HeavisideLambda[x], {x, -2, 2, 4 / 1023}];ListLinePlot[data]dwt = DiscreteWaveletTransform[data, DaubechiesWavelet[3], 5, Padding -> "Reflected"];WaveletScalogram[dwt, {___, 1}, Method -> "Inverse" -> True, ColorFunction -> "AtlanticColors"]data = Table[Piecewise[{{Sin[2π 10 t], 0 ≤ t < (1/4)}, {Sin[2π 25 t], (1/4) ≤ t < (1/2)}, {Sin[2π 50 t], (1/2) ≤ t < (3/4)}, {Sin[2π 100 t], (3/4) ≤ t ≤ 1}}], {t, 0, 1, (1/1023)}];ListLinePlot[data, AspectRatio -> 0.2]cwd = ContinuousWaveletTransform[data, DGaussianWavelet[5], {Automatic, 12}]在更低倍频程上解析更高的频率,在更高倍频程上解析更低的频率:
WaveletScalogram[cwd, ColorFunction -> "RustTones"]属性和关系 (2)
Ticks->Automatic 在垂直轴上标明 DiscreteWaveletData 的精细度:
dwd = DiscreteWaveletTransform[Table[Sin[t^2], {t, 0, 3π, 0.01}], Automatic, 4];WaveletScalogram[dwd, Ticks -> Automatic]WaveletScalogram[dwd, Ticks -> Full]Ticks->Automatic 在垂直轴上标明 ContinuousWaveletData 的精细度:
cwd = ContinuousWaveletTransform[Table[Sin[x^2], {x, 0, 3π, 0.01}]];WaveletScalogram[cwd, Ticks -> Automatic]WaveletScalogram[cwd, Ticks -> Full]巧妙范例 (2)
在 WaveletScalogram 上绘制等高线:
cwd = ContinuousWaveletTransform[Table[Log[2 + Sin[100π Sqrt[t]]], {t, 0, 1, 0.001}]];contours = ListContourPlot[Abs@Reverse[Last /@ cwd[All]], ContourShading -> None, ContourStyle -> Directive[Opacity[0.2], Blue]];Show[WaveletScalogram[cwd], contours]使用 ListPlot3D 在三维空间中可视化小波尺度谱图:
cwd = ContinuousWaveletTransform[Table[Log[2 + Sin[100π Sqrt[t]]], {t, 0, 1, 0.001}]];WaveletScalogram[cwd, ColorFunction -> "SolarColors"]ListPlot3D[Abs@Reverse[Last /@ cwd[All]], PlotRange -> All, Mesh -> None, ColorFunction -> "SolarColors", Ticks -> {Automatic, None, Automatic}, AxesLabel -> {"time", "octaves", "magnitude"}, Boxed -> False]文本
Wolfram Research (2010),WaveletScalogram,Wolfram 语言函数,https://reference.wolfram.com/language/ref/WaveletScalogram.html.
CMS
Wolfram 语言. 2010. "WaveletScalogram." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/WaveletScalogram.html.
APA
Wolfram 语言. (2010). WaveletScalogram. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/WaveletScalogram.html 年
BibTeX
@misc{reference.wolfram_2026_waveletscalogram, author="Wolfram Research", title="{WaveletScalogram}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/WaveletScalogram.html}", note=[Accessed: 02-November-2026]}
BibLaTeX
@online{reference.wolfram_2026_waveletscalogram, organization={Wolfram Research}, title={WaveletScalogram}, year={2010}, url={https://reference.wolfram.com/language/ref/WaveletScalogram.html}, note=[Accessed: 02-November-2026]}