WOLFRAM

Wolfram Language & System Documentation Center

HarmonicMeanFilter[data,r]

filters data by replacing every value by the harmonic mean value in its range-r neighborhood.

HarmonicMeanFilter[data,{r1,r2,…}]

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

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data  
Parameters  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

HarmonicMeanFilter

HarmonicMeanFilter[data,r]

filters data by replacing every value by the harmonic mean value in its range-r neighborhood.

HarmonicMeanFilter[data,{r1,r2,…}]

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

Details

  • HarmonicMeanFilter is used to locally smooth data, particularly when extreme values are present, where the amount of smoothing is dependent on the value of r.
  • The function applied to each range-r neighborhood is HarmonicMean.
  • The data can be any of the following:
  • listarbitrary-rank numerical array
    tseriestemporal data such as TimeSeries, TemporalData, …
    imagearbitrary Image or Image3D object
    audioan Audio object
    videoa Video object
  • For multichannel images and audio signals, HarmonicMeanFilter operates separately on each channel.
  • HarmonicMeanFilter[data,{r1,r2,…}] computes the harmonic mean value in blocks centered on each sample.
  • HarmonicMeanFilter assumes the index coordinate system for lists and images.
  • At the data boundaries, HarmonicMeanFilter uses smaller neighborhoods.

Examples

open all close all

Basic Examples  (3)

Harmonic mean filtering of a list:

Wolfram Language code: HarmonicMeanFilter[{1, 2, 30, 2, 1}, 1]

Filter a TimeSeries:

Wolfram Language code: ts = TemporalData[TimeSeries, {{{2., 1.7273273294285436, 1.3327016210004698, 1.4661458052069154, 1.3882595510720686, 1.3244472923404507, 1.978745787055135, 1.8920720270815607, 1.386172876452206, 1.6751431393445424, 1.9115655094508386, 1.720406 ... 346095457946575, 1.5001955930812627, 1.461132021178403, 1.589839723535445}}, {{0, 1., 0.01}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1];
Wolfram Language code: filtered = HarmonicMeanFilter[ts, .05]
Wolfram Language code: ListLinePlot[{ts, filtered}, PlotLegends -> {"original data", "filtered"}]

Harmonic mean filtering applied to a color image:

Wolfram Language code: HarmonicMeanFilter[[image], 4]

Scope  (13)

Data  (9)

Apply a moving harmonic mean filter to a vector:

Wolfram Language code: HarmonicMeanFilter[ {1, 2, 3, 4, 5}, 1]

Filter a symbolic array:

Wolfram Language code: HarmonicMeanFilter[{a, b, c, d, e, f}, 1]

Filter a 2D array:

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

Filter a TimeSeries:

Wolfram Language code: ts = TemporalData[TimeSeries, {{{2., 1.7273273294285436, 1.3327016210004698, 1.4661458052069154, 1.3882595510720686, 1.3244472923404507, 1.978745787055135, 1.8920720270815607, 1.386172876452206, 1.6751431393445424, 1.9115655094508386, 1.720406 ... 346095457946575, 1.5001955930812627, 1.461132021178403, 1.589839723535445}}, {{0, 1., 0.01}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1];
Wolfram Language code: filtered = HarmonicMeanFilter[ts, .1]
Wolfram Language code: ListLinePlot[{ts, filtered}, PlotLegends -> {"original data", "filtered"}]

Filter a quantity array:

Wolfram Language code: data = Quantity[RandomReal[1, 8], "Meters"]; filtered = HarmonicMeanFilter[data, 1]

Filter an Audio signal:

Wolfram Language code: a = Import["ExampleData/rule30.wav"];
Wolfram Language code: b = HarmonicMeanFilter[a, 15]
Wolfram Language code: AudioPlot[{a, b}]

Filtering a 2D grayscale image:

Wolfram Language code: HarmonicMeanFilter[[image], 3]

Filter video frames:

Wolfram Language code: HarmonicMeanFilter[Video["ExampleData/fish.mp4"], 5]

Harmonic mean filtering of a 3D volume:

Wolfram Language code: HarmonicMeanFilter[[image], 3]

Parameters  (4)

Specify one radius to be used in all directions:

Wolfram Language code: HarmonicMeanFilter[[image], 3]

Increasing the radius will result in smoother images:

Wolfram Language code: Table[Labeled[HarmonicMeanFilter[[image], r], Text["*r* = " <> ToString@r]], {r, {1, 3, 6}}]

Harmonic mean filtering just in the first direction:

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

Second direction:

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

Harmonic mean filtering of a 3D image in the vertical direction only:

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

Filtering of the horizontal planes only:

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

Applications  (3)

Blur a grayscale image:

Wolfram Language code: HarmonicMeanFilter[[image], 4]

Use harmonic mean filtering if your data has outliers:

Wolfram Language code: HarmonicMeanFilter[{1, 2, 3, 4, 100, 6, 7, 8, 9}, 1]
Wolfram Language code: ListLinePlot[%, PlotRange -> All]

Reduce effect of outliers in an image:

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

Properties & Relations  (4)

The harmonic mean is the reciprocal of the mean of reciprocals of the given data:

Wolfram Language code: x = {1, 2, 3, 4, 5}; HarmonicMeanFilter[x, 1] == (1/MeanFilter[(1/x), 1])

For positive data, HarmonicMeanFilter[data,r]≤GeometricMeanFilter[data,r]≤MeanFilter[data,r]:

Wolfram Language code: data = RandomReal[1, 50]; ListLinePlot[{MeanFilter[data, 5], GeometricMeanFilter[data, 5], HarmonicMeanFilter[data, 5]}, PlotRange -> {0, 1}, PlotLegends -> {"mean", "geometric mean", "harmonic mean"}]

Harmonic mean filtering is the same as ArrayFilter with function HarmonicMean:

Wolfram Language code: r = 1; x = {1, 2, -1, 1, 2, 3, 1, -1, 3, 1}; ArrayFilter[HarmonicMean[Flatten[#]]&, x, r, Padding -> None] == HarmonicMeanFilter[x, r][[r + 1 ;; -r - 1]]

Harmonic mean filtering is the same as ImageFilter with function HarmonicMean:

Wolfram Language code: ImageCrop[HarmonicMeanFilter[[image], 1], 3] == ImageCrop[ImageFilter[HarmonicMean[Flatten[#]]&, [image], 1], 3]
Wolfram Research (2008), HarmonicMeanFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html (updated 2025).

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_harmonicmeanfilter, author="Wolfram Research", title="{HarmonicMeanFilter}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_harmonicmeanfilter, organization={Wolfram Research}, title={HarmonicMeanFilter}, year={2025}, url={https://reference.wolfram.com/language/ref/HarmonicMeanFilter.html}, note=[Accessed: 13-June-2026]}