# 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:

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

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

## Creation

### Description

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

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

movAvg = dsp.MovingAverage(Len,Overlap) sets the WindowLength property to Len and the OverlapLength property to Overlap.

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

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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.

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.

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'.

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 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 = movAvg(x) computes the moving average 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 average is computed along each channel.

The object 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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Moving average of the input signal, returned as a vector or a matrix.

When you input a signal of size m-by-n to the object, and if you set Method to 'Sliding window' and SpecifyWindowLength to true, the output has an upper bound size of ceil(m/hop size)-by-n. Hop size is window length − overlap length. In other cases, the output has a size of m-by-n.

When you generate code from this object, the variable-size behavior of the output in the generated code depends on the input frame length and whether the size of the input signal is fixed or variable. For more details, see Code Generation.

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

Initialization

Set up movavgWindow, movavgWindow_overlap, and movavgExp objects. movavgWindow uses the sliding window method with a window length of 50 samples and a default overlap length of 49 samples, which is one sample less than the specified window length. movavgWindow_overlap uses a window length of 50 samples and an overlap length of 45 samples. movavgExp uses the exponentially weighting method with a forgetting factor of 0.95.

Create a time scope for viewing the output.

FrameLength = 1001;
Fs = 1000;
movavgWindow = dsp.MovingAverage(50);
movavgWindow_overlap = dsp.MovingAverage(50,45);
movavgExp = dsp.MovingAverage('Method','Exponential weighting',...
'ForgettingFactor',0.95);
scope  = timescope('SampleRate',[Fs, Fs, Fs/(50-45), Fs],...
'TimeSpanOverrunAction','Scroll',...
'ShowGrid',true,...
'YLimits',[-0.5 1.5]);
title = 'Moving Average';
scope.Title = title;
scope.ChannelNames = {'Original Signal',...
'Sliding window of 50 samples with default overlap',...
'Sliding window of 50 samples with an overlap of 45 samples',...
'Exponential weighting with forgetting factor of 0.95'};

Compute the Average

Generate a ramp signal with an amplitude of 1 and a time span of 2 seconds. Apply the sliding window average and exponentially weighted average to the ramp. View the output in 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 = movavgWindow_overlap(x);
y3 = movavgExp(x);
scope(x,y1,y2,y3);
end

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## References

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

## Version History

Introduced in R2016b

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