4.3. Moving Window Statistics

A moving window is a contiguous subset of a row vector used to compute local statistics. At each step, the window advances to include one new value and leaves off one old value. A statistic is calculated over the values in the window and is placed at the corresponding center position of the returned data. The resulting vector reduces some of the fluctuations found in the original vector. MATLAB provides functions for performing several statistical operations on moving windows. The moving window functions are listed in Moving Window Functions. These functions all use the same syntax.

>> y = movmean(x, k)

Outputs

y – Result of the k-point moving mean applied to the data in x.

Inputs

x – Array of data.

k – Number of points in the window.

Table 4.1 Moving Window Functions

Function	Description
movmin	Moving minimum
movmax	Moving maximum
movsum	Moving sum
movmean	Moving mean
movmedian	Moving median
movstd	Moving standard deviation
movvar	Moving variance

The commands below show how the values are calculated using the movmean function with a window size of 7. Notice that the first three values are calculated with a shortened window size. The full window size is used beginning with the fourth term. The window advances for the first time to not include the first data value at the fifth term. A shortened window size is similarly used at the end of the vector. You can change this behavior by specifying the optional ’Endpoints’ argument. A plot of the original data and the filtered data from the movmean function is shown in figure Fig. 4.2.

>> x = linspace(0, 6, 20);
>> y = 5*x - 0.3*x.^2 + sin(3*x);
>> y1 = movmean(y, 7);
>> y(1:5)
ans =
    0  2.3609  3.9862  4.7626  5.2336
>> y1(1:5)
ans =
    2.7774  3.2687  3.7484  4.3319  5.7502

>> sum(y(1:4))/4
ans =
    2.7774       % y1(1) - startup, short window
>> sum(y(1:5))/5
ans =
    3.2687       % y1(2) - startup, short window
>> sum(y(1:7))/7
ans =
    4.3319       % y1(4) - first full window mean
>> sum(y(2:8))/7
ans =
    5.7502       % y1(5) - window advanced

Fig. 4.2 The moving window mean smooths the data fluctuations.

As with other statistical functions in MATLAB, if \(\bf{X}\) is a matrix, the function is independently applied to the columns of \(\bf{X}\). You can change this behavior by specifying an optional dimension argument. You can also provide an optional flag to specify how NaN values are handled.

Note

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