# dsp.MovingVariance

Moving variance

## Description

The dsp.MovingVariance System object™ computes the moving variance of the input signal along each channel, independently over time. The object uses either the sliding window method or the exponential weighting method to compute the moving variance. In the sliding window method, a window of specified length is moved over the data, sample by sample, and the variance is computed over the data in the window. In the exponential weighting method, the object subtracts each sample of the data from the average, squares the difference, and multiplies the squared result with a weighting factor. The object then computes the variance by adding all the weighted data. For more details on these methods, see Algorithms.

To compute the moving variance of the input:

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

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

## Creation

### Description

MovVar = dsp.MovingVariance returns a moving variance object, MovVar, using the default properties.

example

MovVar = dsp.MovingVariance(Len) sets the WindowLength property to Len.

MovVar = dsp.MovingVariance(Len,Overlap) sets the WindowLength property to Len and the OverlapLength property to Overlap.

example

MovVar = dsp.MovingVariance(Name,Value) specifies additional properties using Name,Value pairs. Unspecified properties have default values.

Example: MovVar = dsp.MovingVariance('Method','Exponential weighting','ForgettingFactor',0.9);

## Properties

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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.

• 'Sliding window' — A window of length specified by SpecifyWindowLength is moved over the input data along each channel. For every sample the window moves by, the object computes the variance over the data in the window.

• 'Exponential weighting' — The object subtracts each sample of the data from the average, squares the difference, and multiplies the squared result with a weighting factor. The object then computes the variance by adding all the weighted data. The magnitude of the weighting factors decreases exponentially as the age of the data increases, never reaching zero.

For more details on these methods, see Algorithms.

Flag to specify a window length, specified as a scalar Boolean.

• true — The length of the sliding window is equal to the value you specify in the WindowLength property.

• false — The length of the sliding window is infinite. In this mode, the variance is computed using the current sample and all past samples.

#### Dependencies

This property applies when you set Method to 'Sliding window'.

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

#### Dependencies

This property applies when you set Method to 'Sliding window' and SpecifyWindowLength to true.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Overlap length between sliding windows, specified as a nonnegative integer. The value of overlap length varies in the range [0, WindowLength − 1]. If not specified, the overlap length is set to WindowLength − 1.

#### Dependencies

This property applies when you set Method to 'Sliding window' and SpecifyWindowLength to true.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Exponential weighting factor, specified as a positive real scalar in the range (0,1].

A forgetting factor of 0.9 gives more weight to the older data than does a forgetting factor of 0.1. A forgetting factor of 1.0 indicates infinite memory. All the past samples are given an equal weight.

Since this property is tunable, you can change its value even when the object is locked.

Tunable: Yes

#### Dependencies

This property applies when you set Method to 'Exponential weighting'.

Data Types: single | double

## Usage

### Description

example

y = movVar(x) computes the moving variance of the input signal, x, using either the sliding window method or exponential weighting method.

### Input Arguments

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Data input, specified as a vector or a matrix. If x is a matrix, each column is treated as an independent channel. The moving variance is computed along each channel. The object also accepts variable-size inputs. Once the object is locked, you can change the size of each input channel, but cannot change the number of channels.

Data Types: single | double
Complex Number Support: Yes

### Output Arguments

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Moving variance of the input signal, returned as a vector or a matrix.

Data Types: single | double
Complex Number Support: Yes

## 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)

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 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

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Compute the moving variance of a noisy square wave signal with varying amplitude using the dsp.MovingVariance object.

Initialization

Set up movvarWindow, movvarWindow_overlap, and movvarExp objects. movvarWindow uses the sliding window method with a window length of 800 samples and a default overlap length of 799 samples, which is 1 sample less than the specified window length. movvarWindow_overlap uses a window length of 800 samples and an overlap length of 700 samples. movvarExp uses the exponentially weighting method with a forgetting factor of 0.999.

Create a time scope for viewing the output.

FrameLength = 100;
Fs = 100;
movvarWindow = dsp.MovingVariance(800);
movvarWindow_overlap = dsp.MovingVariance(800,700);
movvarExp = dsp.MovingVariance('Method','Exponential weighting',...
'ForgettingFactor',0.999);
scope  = timescope('SampleRate',[Fs,Fs,Fs/(800-700),Fs],...
'TimeSpanOverrunAction','Scroll',...
'TimeSpanSource','Property',...
'TimeSpan',1000,...
'ShowGrid',true,...
'BufferLength',1e7,...
'YLimits',[0 7e-4]);
title = 'Moving Variance';
scope.Title = title;
scope.ChannelNames = {'Original Signal',...
'Sliding window of 800 samples with default overlap',...
'Sliding window of 800 samples with an overlap of 700 samples',...
'Exponential weighting with forgetting factor of 0.999'};

Compute the Variance

Generate a noisy square wave signal. Vary the amplitude of the square wave after a given number of frames. Apply the sliding window method and the exponentially weighting method on this signal. The actual variance is np. This value is used while adding noise to the data. Compare the actual variance with the computed variances on the time scope.

count = 1;
noisepower = 1e-4 * [1 2 3 4];
for index = 1:length(noisepower)
np = noisepower(index);
yexp = np*ones(FrameLength,1);
for i = 1:250
x = 1 + sqrt(np) * randn(FrameLength,1);
y1 = movvarWindow(x);
y2 = movvarWindow_overlap(x);
y3 = movvarExp(x);
scope(yexp,y1,y2,y3);
end
end

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## References

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

## Extended Capabilities

Introduced in R2016b

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