dsp.MovingAverage

Moving average

Description

The dsp.MovingAverage System 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, see Algorithms.

To compute the moving average of the input:

Create the dsp.MovingAverage 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

movAvg = dsp.MovingAverage

movAvg = dsp.MovingAverage(Len)

movAvg = dsp.MovingAverage(Name,Value)

Description

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

movAvg = dsp.MovingAverage(Len) sets the WindowLength property to Len.

example

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

Example:

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

Properties

expand all

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

Averaging method, specified as 'Sliding window' or '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 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, 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 average 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]. 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

Syntax

y = movAvg(x)

Description

example

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

Input Arguments

expand all

`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 average 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

expand all

`y` — Moving average
vector | matrix

Moving average 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)

expand all

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

collapse all

Moving Average of Noisy Ramp Signal

Open Script

Compute the moving average of a noisy ramp signal using the dsp.MovingAverage object.

Initialization

Set up movavgWindow and movavgExp objects. movavgWindow uses the sliding window method with a window length of 10. movavgExp uses 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  = timescope('SampleRate',Fs,...
    'TimeSpanOverrunAction','Scroll',...
    '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.

for i = 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

expand all

Sliding Window Method

In the sliding window method, the output for each input sample is the average 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 average 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.

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, see Sliding 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, where N = 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, see Sliding 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.

Documentation

dsp.MovingAverage

Description

Creation

Syntax

Description

Properties

`Method` — Averaging 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 average
vector | matrix

Object Functions

Common to All System Objects

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

Objects

Blocks

Topics

DSP System Toolbox Documentation

Support

Documentation

dsp.MovingAverage

Description

Creation

Syntax

Description

Properties

Method — Averaging 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 average vector | matrix

Object Functions

Common to All System Objects

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

Objects

Blocks

Topics

DSP System Toolbox Documentation

Support

`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]

`x` — Data input
vector | matrix

`y` — Moving average
vector | matrix

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