dsp.MovingStandardDeviation

Moving standard deviation

Description

The dsp.MovingStandardDeviation System object™ computes the moving standard deviation 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 standard deviation. In the sliding window method, a window of specified length is moved over the data, sample by sample, and the object computes the standard deviation over the data in the window. In the exponential weighting method, the object computes the exponentially weighted moving variance, and takes the square root. For more details on these methods, see Algorithms.

To compute the moving standard deviation of the input:

Create the dsp.MovingStandardDeviation object and set its properties.
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

MovStd = dsp.MovingStandardDeviation

MovStd = dsp.MovingStandardDeviation(Len)

MovStd = dsp.MovingStandardDeviation(Name,Value)

Description

MovStd = dsp.MovingStandardDeviation returns a moving standard deviation object, MovStd, using the default properties.

example

MovStd = dsp.MovingStandardDeviation(Len) sets the WindowLength property to Len.

example

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

Example:

MovStd = dsp.MovingStandardDeviation('Method','Exponential
            weighting','ForgettingFactor',0.999);

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.

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

`Method` — Moving standard deviation method
`'Sliding window'` (default) | `'Exponential weighting'`

'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 standard deviation over the data in the window.
'Exponential weighting' — The object computes the exponentially weighted moving variance, and takes the square root.

For more details on these methods, see Algorithms.

`SpecifyWindowLength` — Specify window length
`true` (default) | `false`

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 standard deviation is computed using the current sample and all the past samples.

Dependencies

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

`WindowLength` — Length of the sliding window
4 (default) | positive scalar integer

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.

`ForgettingFactor` — Exponential weighting factor
0.9 (default) | positive real scalar in the range (0,1]

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

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

Syntax

y = movStd(x)

Description

example

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

Input Arguments

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`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 standard deviation 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 you cannot change the number of channels.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

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`y` — Moving standard deviation
vector | matrix

Moving standard deviation 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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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

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Moving Standard Deviation of Noisy Square Wave Signal

Open Script

Compute the moving standard deviation of a noisy square wave signal with varying amplitude using the dsp.MovingStandardDeviation object.

Initialization

Set up movstdWindow and movstdExp objects. movstdWindow uses the sliding window method with a window length of 800. movstdExp uses the exponential weighting method with a forgetting factor of 0.999. Create a time scope for viewing the output.

FrameLength = 100;
Fs = 100;
movstdWindow = dsp.MovingStandardDeviation(800);
movstdExp = dsp.MovingStandardDeviation(...
    'Method','Exponential weighting',...
    'ForgettingFactor',0.999);
scope  = timescope('SampleRate',Fs,...
    'TimeSpanOverrunAction','Scroll',...
    'TimeSpanSource','Property',...
    'TimeSpan',1000,...
    'ShowGrid',true,...
    'BufferLength',1e7,...
    'YLimits',[0 3e-2]);
title = 'Actual (yellow) Sliding Window (blue) Exponentially Weighted (red) standard deviation';
scope.Title = title;

Compute the Standard Deviation

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 exponential weighting method on this signal. The actual standard deviation is sqrt(np). This value is used while adding noise to the data. Compare the actual standard deviation with the computed standard deviation on the time scope.

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

Algorithms

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Sliding Window Method

In the sliding window method, the output at the current sample is the standard deviation of the current sample with respect to the data in the window. 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 standard deviation when the second input sample comes in, the algorithm fills the window with Len – 2 zeros. Len is the length of the window in samples. The data vector, x, is then the two data samples followed by Len – 2 zeros.

When you do not specify the window length, the algorithm chooses an infinite window length. In this mode, the output is the moving standard deviation of the current sample with respect to all the previous samples in the channel.

Consider an example of computing the moving standard deviation 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.

Exponential Weighting Method

In the exponential weighting method, the moving standard deviation is computed recursively using these formulas:

$\begin{array}{l} s_{N, λ} = \sqrt{\frac{1}{v_{N, λ}} \sum_{k = 1}^{N} λ^{N - k} {[x_{k} - {\bar{x}}_{N, λ}]}^{2}} \\ v_{N, λ} = \frac{2 λ (1 - λ^{N - 1})}{(1 - λ) (1 + λ)} \end{array}$

$s_{N, λ}$ — Moving standard deviation of the current data sample with respect to the rest of the data.
${[x_{k} - {\bar{x}}_{N, λ}]}^{2}$ — Difference between each data sample and the average of the data, squared.
$\sum_{k = 1}^{N} λ^{N - k} {[x_{k} - {\bar{x}}_{N, λ}]}^{2}$ — Difference between each data sample and the average of the data, squared and multiplied with the forgetting factor. All the squared terms are added.
$\frac{1}{v_{N, λ}}$ — Weighting factor applied to the sum.
λ — Forgetting factor.

As the age of the data increases, the magnitude of the weighting factor decreases exponentially and never reaches zero. In other words, the recent data has more influence on the current standard deviation than the older data.

The value of the forgetting factor determines the rate of change of the weighting factors. 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 previous samples are given an equal weight.

Consider an example of computing the moving standard deviation using the exponential weighting method. The forgetting factor is 0.9.

References

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

Documentation

dsp.MovingStandardDeviation

Description

Creation

Syntax

Description

Properties

`Method` — Moving standard deviation method
`'Sliding window'` (default) | `'Exponential weighting'`

`SpecifyWindowLength` — Specify window length
`true` (default) | `false`

Dependencies

`WindowLength` — Length of the sliding window
4 (default) | positive scalar integer

Dependencies

`ForgettingFactor` — Exponential weighting factor
0.9 (default) | positive real scalar in the range (0,1]

Dependencies

Usage

Syntax

Description

Input Arguments

`x` — Data input
vector | matrix

Output Arguments

`y` — Moving standard deviation
vector | matrix

Object Functions

Common to All System Objects

Examples

Moving Standard Deviation of Noisy Square Wave Signal

Algorithms

Sliding Window Method

Exponential Weighting Method

References

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

Objects

Blocks

Topics

DSP System Toolbox Documentation

Support

Documentation

dsp.MovingStandardDeviation

Description

Creation

Syntax

Description

Properties

Method — Moving standard deviation method 'Sliding window' (default) | 'Exponential weighting'

SpecifyWindowLength — Specify window length true (default) | false

Dependencies

WindowLength — Length of the sliding window 4 (default) | positive scalar integer

Dependencies

ForgettingFactor — Exponential weighting factor 0.9 (default) | positive real scalar in the range (0,1]

Dependencies

Usage

Syntax

Description

Input Arguments

x — Data input vector | matrix

Output Arguments

y — Moving standard deviation vector | matrix

Object Functions

Common to All System Objects

Examples

Moving Standard Deviation of Noisy Square Wave Signal

Algorithms

Sliding Window Method

Exponential Weighting Method

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

See Also

Objects

Blocks

Topics

DSP System Toolbox Documentation

Support

`Method` — Moving standard deviation method
`'Sliding window'` (default) | `'Exponential weighting'`

`SpecifyWindowLength` — Specify window length
`true` (default) | `false`

`WindowLength` — Length of the sliding window
4 (default) | positive scalar integer

`ForgettingFactor` — Exponential weighting factor
0.9 (default) | positive real scalar in the range (0,1]

`x` — Data input
vector | matrix

`y` — Moving standard deviation
vector | matrix

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.