# Moving Average

Moving average

• Library:
• DSP System Toolbox / Statistics

## Description

The Moving Average block computes the moving average of the input signal along each channel independently over time. The block uses the sliding window method or the exponential weighting method to compute the moving average. In the sliding window method, a window of specified length moves over the data sample by sample, and the block computes the average over the data in the window. In the exponential weighting method, the block multiplies the data samples with a set of weighting factors and then sums the weighted data to compute the average. For more details on these methods, see Algorithms.

## Ports

### Input

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The block computes the moving average of the data specified at this input port. Specify real- or complex-valued multichannel inputs of the size m-by-n, where m ≥ 1 and n ≥ 1.

When the Allow arbitrary frame length for fixed-size input signals parameter appears and is not selected, and you input a fixed-size signal, the frame length must be a multiple of the hop size (window length − overlap length). In all other cases, the input frame length can be arbitrary.

The block accepts variable-size inputs (frame length changes during simulation). When you input a variable-size signal, the frame length of the signal can be arbitrary.

This port is unnamed until you set Method to `Exponential weighting` and select the Specify forgetting factor from input port parameter.

Data Types: `single` | `double`
Complex Number Support: Yes

The forgetting factor determines how much weight past data is given. 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.

#### Dependencies

This port appears when you set Method to ```Exponential weighting``` and select the Specify forgetting factor from input port parameter.

Data Types: `single` | `double`

### Output

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Moving average, returned as a vector or a matrix. The block computes the moving average based on the Method parameter settings using either the sliding window method or the exponential weighting method. For more details, see Algorithms.

This table provides more details on the dimensions of the output signal.

Input SignalInput DimensionsOutput Dimensions When Allow arbitrary frame length for fixed-size input signals AppearsOutput Dimensions When Allow arbitrary frame length for fixed-size input signals Does Not Appear
Fixed-size signalm-by-n, where m is a multiple of the hop size (window length − overlap length)

(m/hop size)-by-n

m-by-n

Fixed-size signalm-by-n, where m is not a multiple of the hop size (window length − overlap length)

`ceil`(m/hop size)-by-n when you select Allow arbitrary frame length for fixed-size input signals

If you do not select Allow arbitrary frame length for fixed-size input signals, the block errors.

m-by-n

Variable-size signalm-by-n `ceil`(m/hop size)-by-n

m-by-n

When the output has an upper bound size of `ceil`(m/hop size)-by-n, during simulation, the size of the first dimension varies within this bound and the size of the second dimension remains constant. For an example that shows this behavior, see Compute Moving Average of Noisy Step Signal.

Data Types: `single` | `double`
Complex Number Support: Yes

## Parameters

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If a parameter is listed as tunable, then you can change its value during simulation.

• `Sliding window` — A window of length Window length moves over the input data along each channel. For every sample the window moves over, the block computes the average over the data in the window.

• `Exponential weighting` — The block multiplies the samples by a set of weighting factors. The magnitude of the weighting factors decreases exponentially as the age of the data increases, but the magnitude never reaches zero. To compute the average, the algorithm sums the weighted data.

When you select this check box, the length of the sliding window is equal to the value you specify in . When you clear this check box, the length of the sliding window is infinite. In this mode, the block computes the average of the current sample and all previous samples in the channel.

#### Dependencies

To enable this parameter, set Method to ```Sliding window```.

Specifies the length of the sliding window in samples.

#### Dependencies

To enable this parameter, set Method to ```Sliding window``` and select the check box.

Specify the overlap length between sliding windows as a nonnegative integer. The value of overlap length varies in the range [0, Window length − 1].

#### Dependencies

To enable this parameter, set Method to ```Sliding window``` and select the check box.

Specify whether fixed-size input signals (whose size does not change during simulation) can have an arbitrary frame length, where the frame length does not have to be a multiple of the hop size. Hop size is defined as Window lengthOverlap length. The block uses this parameter setting only for fixed-size input signals and ignores this parameter if the input has a variable-size.

When the input signal is a variable-size signal, the signal can have arbitrary frame length, that is, the frame length does not have to be a multiple of the hop size.

For fixed-size input signals, if you:

• Select the Allow arbitrary frame length for fixed-size input signals parameter, the frame length of the signal does not have to be a multiple of the hop size. If the input is not a multiple of the hop size, then the output is generally a variable-size signal. Therefore, to support arbitrary input size, the block must also support variable-size operations, which you can enable by selecting the Allow arbitrary frame length for fixed-size input signals parameter.

• Clear the Allow arbitrary frame length for fixed-size input signals parameter, the input frame length must be a multiple of the hop size.

#### Dependencies

To enable this parameter, set Method to ```Sliding window``` and select the check box.

When you select this check box, the forgetting factor is input through the lambda port. When you clear this check box, the forgetting factor is specified on the block dialog through the Forgetting factor parameter.

#### Dependencies

To enable this parameter, set Method to ```Exponential weighting```.

The forgetting factor determines how much weight past data is given. 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.

Tunable: Yes

#### Dependencies

To enable this parameter, set Method to ```Exponential weighting``` and clear the Specify forgetting factor from input port check box.

Specify the type of simulation to run as one of the following:

• `Code generation` –– Simulate model using generated C code. The first time you run a simulation, Simulink® generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time but provides faster simulation speed than `Interpreted execution`.

• `Interpreted execution` –– Simulate model using the MATLAB®  interpreter. This option shortens startup time but has slower simulation speed than `Code generation`.

## Block Characteristics

 Data Types `double` | `single` Multidimensional Signals `No` Variable-Size Signals `Yes`

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## Version History

Introduced in R2016b

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