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StandardDeviationFilter[data,r]

filters data by replacing every value by the standard deviations of the values in its range-r neighborhood.

StandardDeviationFilter[data,{r1,r2,…}]

uses ri for filtering the ^(th)dimension in data.

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Basic Examples  
Scope  
Data  
Parameters  
Applications  
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StandardDeviationFilter

StandardDeviationFilter[data,r]

filters data by replacing every value by the standard deviations of the values in its range-r neighborhood.

StandardDeviationFilter[data,{r1,r2,…}]

uses ri for filtering the ^(th)dimension in data.

Details

Examples

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Basic Examples  (3)

Moving standard deviation of a list:

Wolfram Language code: StandardDeviationFilter[ {0, 0, 1, 1, 1, 1, 1, 0, 0, 0}, 1]

Filter a TimeSeries:

Wolfram Language code: ts = TemporalData[TimeSeries, {{{0., -0.27267267057145633, -0.6672983789995302, -0.5338541947930846, -0.6117404489279314, -0.6755527076595494, -0.02125421294486496, -0.10792797291843935, -0.6138271235477938, -0.3248568606554575, -0.08843449054 ... 2053424, -0.49980440691873723, -0.5388679788215971, -0.4101602764645551}}, {{0, 1., 0.01}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1];
Wolfram Language code: filtered = StandardDeviationFilter[ts, .1]
Wolfram Language code: ListLinePlot[{ts, filtered}, PlotLegends -> {"original data", "filtered"}]

Apply standard deviation filtering to a color image:

Wolfram Language code: StandardDeviationFilter[[image], 4]// ImageAdjust

Scope  (12)

Data  (7)

Standard deviation filtering of a numeric vector:

Wolfram Language code: StandardDeviationFilter[{0, 1, 3, 8, 2, 6}, 1]
Wolfram Language code: N[%]

Standard deviation filtering of a 2D array:

Wolfram Language code: StandardDeviationFilter[(⁠| | | | | | - | - | - | - | | 0 | 3 | 8 | 2 | | 7 | 6 | 9 | 6 | | 5 | 8 | 4 | 0 | | 3 | 5 | 1 | 6 |⁠), 1]//N//MatrixForm

Filtering of a list of Quantity objects:

Wolfram Language code: data = {Quantity[9, "Feet"], Quantity[86, "Inches"], Quantity[27.1, "Meters"], Quantity[79, "Feet"], Quantity[90, "Feet"], Quantity[41, "Inches"], Quantity[99, "Inches"], Quantity[6, "Feet"], Quantity[38, "Feet"], Quantity[89, "Feet"], Quantity[53, "Feet"], Quantity[85, "Meters"], Quantity[92, "Meters"], Quantity[95, "Meters"], Quantity[49, "Feet"]};
Wolfram Language code: ListLinePlot[{data, StandardDeviationFilter[data, 3]}]

Filter an Audio signal:

Wolfram Language code: a = Import["ExampleData/rule30.wav"]; b = StandardDeviationFilter[a, 35]
Wolfram Language code: AudioPlot[{a, b}]

Filtering a 2D grayscale image:

Wolfram Language code: StandardDeviationFilter[[image], 5]//ImageAdjust

Filter video frames:

Wolfram Language code: StandardDeviationFilter[Video["ExampleData/fish.mp4"], 3]

Standard deviation filtering of a 3D image:

Wolfram Language code: StandardDeviationFilter[[image], 2]

Parameters  (5)

Specify one radius to be used in all directions:

Wolfram Language code: StandardDeviationFilter[[image], 1]

Increasing the radius will result in larger image streaks and patches:

Wolfram Language code: Table[Labeled[StandardDeviationFilter[[image], r], Text["*r* = " <> ToString@r]], {r, {1, 2, 4}}]

Standard deviation filtering just in the first direction:

Wolfram Language code: StandardDeviationFilter[[image], {5, 0}]

Standard deviation filtering just in the second direction:

Wolfram Language code: StandardDeviationFilter[[image], {0, 5}]

Standard deviation filtering of a 3D image in the vertical direction only:

Wolfram Language code: StandardDeviationFilter[[image], {4, 0, 0}]

Filtering of a 3D image in the horizontal planes only:

Wolfram Language code: StandardDeviationFilter[[image], {0, 4, 4}]

Applications  (2)

Find busy regions in a satellite image:

Wolfram Language code: StandardDeviationFilter[[image], 2]// ImageAdjust

Use a standard deviation filter to find edges:

Wolfram Language code: StandardDeviationFilter[[image], 1]
Wolfram Research (2008), StandardDeviationFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/StandardDeviationFilter.html (updated 2025).

Text

Wolfram Research (2008), StandardDeviationFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/StandardDeviationFilter.html (updated 2025).

CMS

Wolfram Language. 2008. "StandardDeviationFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/StandardDeviationFilter.html.

APA

Wolfram Language. (2008). StandardDeviationFilter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/StandardDeviationFilter.html

BibTeX

@misc{reference.wolfram_2026_standarddeviationfilter, author="Wolfram Research", title="{StandardDeviationFilter}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/StandardDeviationFilter.html}", note=[Accessed: 15-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_standarddeviationfilter, organization={Wolfram Research}, title={StandardDeviationFilter}, year={2025}, url={https://reference.wolfram.com/language/ref/StandardDeviationFilter.html}, note=[Accessed: 15-June-2026]}