dsp.MovingAverage System object

Moving average

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Description

Thedsp.MovingAverageSystem object™ computes the moving average 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 average. In the sliding window method, a window of specified length is moved over the data, sample by sample, and the average is computed over the data in the window. In the exponential weighting method, the object multiplies the data samples with a set of weighting factors. The average is computed by summing the weighted data. For more details on these methods, seeAlgorithms.

The object accepts multichannel inputs, that is,m-by-nsize inputs, wherem≥ 1, andn> 1. The object also accepts variable-size inputs. Once the object is locked, you can change the size of each input channel. However, the number of channels cannot change. This object supports C and C++ code generation.

To compute the moving average of the input:

Create adsp.MovingAverageobject and set the properties of the object.
Callstepto compute the moving average.

Note

Alternatively, instead of using thestep方法来执行操作defined by the System object, you can call the object with arguments, as if it were a function. For example,y = step(obj,x)andy = obj(x)perform equivalent operations.

Construction

movAvg = dsp.MovingAveragereturns a moving average object,movAvg, using the default properties.

movAvg = dsp.MovingAverage(Len)sets theWindowLengthproperty toLen.

movAvg = dsp.MovingAverage(Name,Value)specifies additional properties usingName,Valuepairs. Unspecified properties have default values.

Example:

movAvg = dsp.MovingAverage('Method','Exponential weighting','ForgettingFactor',0.9);

Properties

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`Method`—Averaging method
`'Sliding window'`(default) |`'Exponential weighting'`

Averaging method, specified as'Sliding window'or'Exponential weighting'.

'Sliding window'— A window of length specified bySpecifyWindowLengthis moved over the input data along each channel. For every sample the window moves by, the object computes the average over the data in the window.
'Exponential weighting'— The object multiplies the samples with a set of weighting factors. The magnitude of the weighting factors decreases exponentially as the age of the data increases, never reaching zero. To compute the average, the algorithm sums the weighted data.

For more details on these methods, seeAlgorithms.

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

This property applies when you setMethodto'Sliding window'.

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

Length of the sliding window, specified as a positive scalar integer. This property applies when you setMethodto'Sliding window'andSpecifyWindowLengthtotrue.

`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]. This property applies when you setMethodto'Exponential weighting'. 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. This property is tunable. You can change its value even when the object is locked.

Methods

reset	Reset internal states ofSystem object
step	Moving average of input signal

Common to All System Objects
`release`	Allow System object property value changes

Examples

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Moving Average of Noisy Ramp Signal

Open Live Script

计算一个嘈杂的斜坡信号的移动平均线using thedsp.MovingAverageobject.

Initialization

Set upmovavgWindowandmovavgExpobjects.movavgWindowuses the sliding window method with a window length of 10.movavgExpuses the exponentially weighting method with a forgetting factor of 0.9. Create a time scope for viewing the output.

FrameLength = 1001; Fs = 1000; movavgWindow = dsp.MovingAverage(10); movavgExp = dsp.MovingAverage('Method','Exponential weighting',...'ForgettingFactor',0.9); scope = dsp.TimeScope('SampleRate',Fs,...'TimeSpanOverrunAction','Scroll',...'TimeSpan',2,...'ShowGrid',true,...'YLimits',[-0.5 1.5]); title ='Sliding Window Average(blue) and Exponentially Weighted Average(red)'; scope.Title = title;

Compute the Average

Generate a ramp signal with an amplitude of 1.0 and a time span of 2 seconds. Apply the sliding window average and exponentially weighted average to the ramp. View the output on the time scope.

fori = 1:500 t = (0:0.001:1)'; unitstep = t>=0; ramp = t.*unitstep; x = ramp + 0.1 * randn(FrameLength,1); y1 = movavgWindow(x); y2 = movavgExp(x); scope([x,y1,y2]);end

Algorithms

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Sliding Window Method

In the sliding window method, the output for each input sample is the average of the current sample and theLen– 1 previous samples.Lenis the length of the window. To compute the firstLen– 1 outputs, when the window does not have enough data yet, the algorithm fills the window with zeros. As an example, to compute the average when the second input sample comes in, the algorithm fills the window withLen– 2 zeros. The data vector,x, is then the two data samples followed byLen– 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 average of the current sample and all the previous samples in the channel.

For an example, seeSliding Window Method and Exponential Weighting Method.

Exponential Weighting Method

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

$\begin{array}{l} w_{N, λ} = λ w_{N - 1, λ} + 1 \\ {\bar{x}}_{N, λ} = (1 - \frac{1}{w_{N, λ}}) {\bar{x}}_{N - 1, λ} + (\frac{1}{w_{N, λ}}) x_{N} \end{array}$

${\bar{x}}_{N, λ}$ — Moving average at the current sample
$x_{N}$ — Current data input sample
${\bar{x}}_{N - 1, λ}$ — Moving average at the previous sample
λ — Forgetting factor
$w_{N, λ}$ — Weighting factor applied to the current data sample
$(1 - \frac{1}{w_{N, λ}}) {\bar{x}}_{N - 1, λ}$ — Effect of the previous data on the average

For the first sample, whereN= 1, the algorithm chooses $w_{N, λ}$ = 1. For the next sample, the weighting factor is updated and used to compute the average, as per the recursive equation. 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 average 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 the previous samples are given an equal weight.

For an example, seeSliding Window Method and Exponential Weighting Method.

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:

SeeSystem Objects in MATLAB Code Generation(MATLAB Coder).

Documentation

dsp.MovingAverage System object

Description

Note

Construction

Properties

`Method`—Averaging 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]

Methods

Examples

Moving Average of Noisy Ramp 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

System Objects

Blocks

Topics

Introduced in R2016b

DSP System Toolbox Documentation

万博1manbetx

Try MATLAB, Simulink, and Other Products

Documentation

dsp.MovingAverage System object

Description

Note

Construction

Properties

Method—Averaging method'Sliding window'(default) |'Exponential weighting'

SpecifyWindowLength—Specify window lengthtrue(default) |false

WindowLength—Length of the sliding window4(default) |positive scalar integer

ForgettingFactor—Exponential weighting factor0.9(default) |positive real scalar in the range (0,1]

Methods

Examples

Moving Average of Noisy Ramp Signal

Algorithms

Sliding Window Method

Exponential Weighting Method

References

Extended Capabilities

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

See Also

System Objects

Blocks

Topics

Introduced in R2016b

DSP System Toolbox Documentation

万博1manbetx

Try MATLAB, Simulink, and Other Products

`Method`—Averaging 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]

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