dsp.MedianFilter

R2026b

Median filter

Description

The dsp.MedianFilter System object™ computes the moving median of the input signal along each channel, independently over time. The object uses the sliding window method to compute the moving median. In this method, a window of specified length is moved over each channel, sample by sample, and the object computes the median of the data in the window.

You can make the window length tunable by setting the EnableTunableWindowLength property to true. In this mode, use the TunableWindowLength property to change the window length even after you pass some data to the object and the object is locked. The MaxWindowLength property specifies the maximum allowed window length. (since R2026b)

For more details, see Algorithms.

The dsp.MedianFilter object and the movmedian function both compute the moving median of the input signal. However, the object can process large streams of real-time data and handle system states automatically. The function performs one-time computations on data that is readily available and cannot handle system states. For a comparison between the two, see System Objects vs MATLAB Functions.

To compute the moving median of the input:

1. Create the dsp.MedianFilter object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

medFilt = dsp.MedianFilter

medFilt = dsp.MedianFilter(Len)

medFilt = dsp.MedianFilter(PropertyName=Value)

Description

medFilt = dsp.MedianFilter returns a median filter object, medFilt, using the default properties.

medFilt = dsp.MedianFilter(Len) sets the WindowLength property to Len.

medFilt = dsp.MedianFilter(PropertyName=Value) sets properties using one or more name-value arguments. For example, to enable tunable window length, set EnableTunableWindowLength to true and to specify a maximum window length of 30, set MaxWindowLength to 30.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

EnableTunableWindowLength — Option to enable tunable window length

false (default) | true

Since R2026b

Option to enable tunable window length, specified as a scalar boolean.

• true — The window length is tunable, that is, you can change its value even after you pass some data to the object and the object is locked. Use the TunableWindowLength property to specify the window length.

• false — The window length is not tunable. Use the WindowLength property to specify a fixed window length.

WindowLength — Length of sliding window

5 (default) | positive integer

Length of the sliding window in samples, specified as a positive integer. You cannot tune the value of this property after the object is locked. To tune the window length, set the EnableTunableWindowLength property to true.

Dependencies

This property applies when you set EnableTunableWindowLength to false. (since R2026b)

TunableWindowLength — Tunable sliding window length

5 (default) | positive integer in the range [1, MaxWindowLength]

Since R2026b

Tunable sliding window length in samples, specified as a positive integer in the range [1, MaxWindowLength]. You can change the value of this property even when the object is locked.

When you set AutoAdjustInvalidWindowLength to true, the object adjusts invalid values and issues a warning:

• If the tunable window length value is greater than MaxWindowLength, the object uses MaxWindowLength.

• If the tunable window length value is less than 1, the object uses 1.

• If the tunable window length value is not an integer, the object uses the floored value.

When you set AutoAdjustInvalidWindowLength to false, the object throws an error for invalid values.

Tunable: Yes

Dependencies

This property applies when you set EnableTunableWindowLength to true.

MaxWindowLength — Maximum window length

20 (default) | positive integer

Since R2026b

Maximum value of the tunable window length, specified as a positive integer. The TunableWindowLength property must be less than or equal to this value.

Dependencies

This property applies when you set EnableTunableWindowLength to true.

AutoAdjustInvalidWindowLength — Automatically adjust invalid window length

true (default) | false

Since R2026b

Option to automatically adjust invalid window length values, specified as a scalar boolean.

• true — The object adjusts invalid TunableWindowLength values and issues a warning.

  • If the tunable window length value is greater than MaxWindowLength, the object sets its value to MaxWindowLength.

  • If the tunable window length value is less than 1, the object sets its value to 1.

  • If the tunable window length value is not an integer, the object uses the floored value.

• false — The object throws an error when the tunable window length value is invalid.

Dependencies

This property applies when you set EnableTunableWindowLength to true.

Usage

Syntax

y = medFilt(x)

Description

y = medFilt(x) computes the moving median of the input signal, x, using the sliding window method.

Input Arguments

x — Data input

vector | matrix

Data input, specified as a vector or a matrix. If x is a matrix, each column is treated as an independent channel. The moving median is computed along each channel. The object accepts multichannel inputs, that is, m-by-n size inputs, where m ≥ 1, and n > 1. m is the number of samples in each frame (or channel), and n is the number of channels.

The object also accepts variable-size inputs. Once the object is locked, you can change the size of each input channel, but you cannot change the number of channels.

Data Types: single | double

Output Arguments

y — Filtered signal

vector | matrix

Filtered signal, returned as a vector or a matrix. The size and data type of the output matches the size and data type of the input.

Data Types: single | double

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Remove High-Frequency Noise Using Median Filter

Filter high-frequency noise from a noisy sine wave signal using a median filter. Compare the performance of the median filter with an averaging filter.

Initialization

Set up a dsp.MedianFilter object, medFilt, and a dsp.MovingAverage object, movavgWin. These objects use the sliding window method with a window length of 7. Create a time scope for viewing the output.

Fs = 1000;
medFilt = dsp.MedianFilter(7);
movavgWin = dsp.MovingAverage(7);
scope  = timescope(SampleRate=Fs,...
    TimeSpanSource="Property",...
    TimeSpanOverrunAction="Scroll",...
    TimeSpan=1,ShowGrid=true,...
    YLimits=[-3 3],...
    LayoutDimensions=[3 1],...
    NumInputPorts=3);
scope.ActiveDisplay = 1;
scope.Title = "Signal + Noise";
scope.ActiveDisplay = 2;
scope.Title = "Moving Average Output (Window Length = 7)";
scope.ActiveDisplay = 3;
scope.Title = "Median Filter Output (Window Length = 7)";

FrameLength = 256;
count = 1;
sine = dsp.SineWave(SampleRate=Fs,Frequency=10,...
    SamplesPerFrame=FrameLength);

Filter the Noisy Sine Wave

Generate a noisy sine wave signal with a frequency of 10 Hz. Apply the median filter and the moving average object to the signal. View the output on the time scope.

for i = 1:500
    hfn = 3 * (rand(FrameLength,1) < 0.02);
    x = sine() + 1e-2 * randn(FrameLength,1) + hfn;
    y1 = movavgWin(x);
    y2 = medFilt(x);
    scope(x,y1,y2);
end

The median filter removes the high-frequency noise more effectively than the moving average object does.

Remove High-Frequency Noise from Gyroscope Data

This example shows how to remove the high-frequency outliers from a streaming signal using the dsp.MedianFilter System object.

Use the dsp.MatFileReader System object to read the gyroscope MAT file. The gyroscope MAT file contains 3 columns of data, with each column containing 7140 samples. The three columns represent the X-axis, Y-axis, and Z-axis data from the gyroscope motion sensor. Choose a frame size of 714 samples so that each column of the data contains 10 frames. The dsp.MedianFilter System object uses a window length of 10. Create a timescope object to view the filtered output.

reader = dsp.MatFileReader(SamplesPerFrame=714,...
    Filename="LSM9DS1gyroData73.mat",...
    VariableName="data");
medFilt = dsp.MedianFilter(10);
scope = timescope(NumInputPorts=1,...
    SampleRate=119,...
    YLimits=[-300 300],...
    ChannelNames={"Input","Filtered Output"},...
    TimeSpanSource="Property",...
    TimeSpan=60,ShowLegend=true);

Filter the gyroscope data using the dsp.MedianFilter System object. View the filtered Z-axis data in the time scope.

for i = 1:10
    gyroData = reader();
    filteredData = medFilt(gyroData);
    scope([gyroData(:,3),filteredData(:,3)]);
end

The original data contains several outliers. Zoom in on the data to confirm that the median filter removes all the outliers.

Adaptive Median Filtering with Tunable Window Length

Since R2026b

Filter a noisy sinusoidal signal using a median filter and adapt the window length based on the noise level. Use a shorter window when the noise is light and a longer window when the noise is heavy.

Create Input Signal

Create a sine wave signal with a frequency of 5 Hz. Set the sampling rate to 1000 Hz and the frame size to 256 samples.

Fs = 1000;
frameSize = 256;
numFrames = 40;
sine = dsp.SineWave(Frequency=5,SampleRate=Fs,...
    SamplesPerFrame=frameSize)

sine = 
  dsp.SineWave with properties:

          Amplitude: 1
          Frequency: 5
        PhaseOffset: 0
      ComplexOutput: false
             Method: 'Trigonometric function'
    SamplesPerFrame: 256
         SampleRate: 1000
     OutputDataType: 'double'

Create Median Filter Object

Create a dsp.MedianFilter object with tunable window length enabled. Set the maximum window length to 31 and the initial tunable window length to 5. Enable auto-adjustment to handle edge cases.

medFilt = dsp.MedianFilter(EnableTunableWindowLength=true,...
    TunableWindowLength=5,...
    MaxWindowLength=31,...
    AutoAdjustInvalidWindowLength=true)

medFilt = 
  dsp.MedianFilter with properties:

        EnableTunableWindowLength: true
              TunableWindowLength: 5
                  MaxWindowLength: 31
    AutoAdjustInvalidWindowLength: true

Create a timescope object to view the filtered output.

scope = timescope(SampleRate=Fs,...
    TimeSpanSource="property",TimeSpan=numFrames*frameSize/Fs,...
    TimeSpanOverrunAction="Scroll",...
    ShowGrid=true,YLimits=[-4 4],ChannelNames={"Input Noisy Signal","Filtered Output"},...
    LayoutDimensions=[2 1],NumInputPorts=2);

Apply Adaptive Median Filtering

The intensity of noise increases over time. At each frame, add impulse noise whose density grows linearly. Adapt the window length proportionally to the noise density so that heavier noise is filtered with a longer window.

As the noise density increases over time, the adaptive median filter uses a progressively longer window to remove the impulse noise while preserving the underlying sine wave.

View the noisy signal and the filtered signal in the time scope.

for index = 1:numFrames
    x = sine();
    noiseDensity = 0.01 + 0.09*(index/numFrames);
    impulseNoise = 3*(rand(frameSize,1) < noiseDensity).*sign(randn(frameSize,1));
    noisySignal = x + impulseNoise;
    wl = round(5 + 26*(index/numFrames));
    medFilt.TunableWindowLength = wl;
    y = medFilt(noisySignal);
    scope(noisySignal,y)
end

Generate Code for Median Filter with Tunable Window Length

Since R2026b

Generate C code for a median filter with a tunable window length parameter. Verify that the window length appears as a tunable parameter in the generated code.

Create Entry-Point Function

Create an entry-point function that instantiates a dsp.MedianFilter object with tunable window length enabled. The function accepts a data input and a tunable window length value.

type medianFilterTunableWL.m

function y = medianFilterTunableWL(x,wl) %#codegen
%medianFilterTunableWL Median filter with tunable window length
%   y = medianFilterTunableWL(x,wl) filters the input x using a median
%   filter whose window length can be changed at runtime.

persistent medFilt
if isempty(medFilt)
    medFilt = dsp.MedianFilter(EnableTunableWindowLength=true,...
        MaxWindowLength=31,...
        AutoAdjustInvalidWindowLength=true);
end

medFilt.TunableWindowLength = wl;
y = medFilt(x);
end

Generate C Code

Generate C code for the entry-point function using codegen. Specify the input data as a 256-by-1 column vector of doubles and the window length as a scalar double.

codegen medianFilterTunableWL -args {zeros(256,1),0} -config:lib -report

Code generation successful: View report

Verify Tunable Parameter in Generated Code

Inspect the generated code to verify that TunableWindowLength appears as a parameter that can be changed at runtime without regenerating code.

The generated code contains the TunableWindowLength field in the persistent object state, confirming that you can change the window length at runtime in the deployed code.

Algorithms

Sliding Window Method

In the sliding window method, the output for each input sample is the median of the current sample and the Len−1 previous samples. Len is the length of the window in samples. To compute the first Len−1 outputs, when the window does not have enough data yet, the algorithm fills the window with zeros. As an example, to compute the median value when the second input sample comes in, the algorithm fills the window with Len−2 zeros. The data vector, x, is then the two data samples followed by Len−2 zeros. This object performs median filtering on the input data over time.

Consider an example of computing the moving median of a streaming input data using the sliding window method. The algorithm uses a window length of 4. With each input sample that comes in, the window of length 4 moves along the data.

Tunable Window Length Algorithm

When you specify the window length to be tunable, the median filter algorithm maintains an internal buffer of size MaxWL−1 to store past input samples, where MaxWL is the maximum window length. At each time step, the median filter algorithm performs these operations:

1. Concatenates the buffer with the current input to form an extended data sequence.

2. Extracts the most recent window length samples from the extended data sequence.

3. Computes the moving median over the extracted samples using a sliding window and discards the endpoints.

4. Stores the most recent MaxWL−1 samples in the buffer for the next time step.

This approach allows you to change the window length at each time step while the algorithm maintains continuity of the output signal.

References

[1] Bodenham, Dean. “Adaptive Filtering and Change Detection for Streaming Data.” PH.D. Thesis. Imperial College, London, 2012.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

This object supports C and C++ code generation.

Version History

Introduced in R2016b

R2026b: Tunable window length

You can now change the window length even after the object is locked by setting the EnableTunableWindowLength property to true. Use the TunableWindowLength property to specify the window length. The MaxWindowLength property defines the upper bound for the tunable window length. Use the AutoAdjustInvalidWindowLength property to control whether invalid window length values are automatically adjusted with a warning or cause an error.