dsp.MedianFilter

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. 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(Name,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(Name,Value) specifies the WindowLength property using a Name,Value pair.

Example:

movMin = dsp.MedianFilter('WindowLength',5);

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.

WindowLength — Length of sliding window

5 (default) | positive scalar integer

Length of the sliding window in samples, specified as a positive scalar integer.

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.

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.

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