MATLAB movmean and movmedian Function

Sep. 26, 2022

Introduction

MATLAB提供移动（局部）均值和移动（局部）中值的计算函数movmean和movmedian，它们的属性设置基本一致。本文以movmean函数为例进行详细地解释。


Examples

Centered Moving Average of Vector

Example 1: movmean(A, 3)

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clc, clear, close all

A = [4 8 6 -1 -2 -3 -1 3 4 5];
M1 = movmean(A, 3);

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M1 =
    6.0000    6.0000    4.3333    1.0000   -2.0000   -2.0000   -0.3333    2.0000    4.0000    4.5000

image-20220925224512539

当设置window为3时，默认情况下不减少数组的维度，第一个和最后一个窗口的长度为2。

Example 2: movmean(A, 3, 'Endpoints', 'discard')

该函数在默认情况下，'Endpoint'属性是'shrink'，表示“Shrink the window size near the endpoints of the input to include only existing elements”。如果想要软件只计算Full-Window Averages，可以进行下面的设置，表示“Do not output any averages when the window does not completely overlap with existing elements”：

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M2 = movmean(A, 3, 'Endpoints', 'discard');

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M2 =
    6.0000    4.3333    1.0000   -2.0000   -2.0000   -0.3333    2.0000    4.0000

此时，数组的维度减少到$(10-(3-1))$：

image-20220925230850480

Example 3: movmean(A, 4)

如果窗口的长度为偶数：

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M3 = movmean(A, 4);

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M3 =
    6.0000    6.0000    4.2500    2.7500         0   -1.7500   -0.7500    0.7500    2.7500    4.0000

image-20220925231251841

Example 4: movmean(A, 4, 'Endpoints', 'discard')

同样地，只计算Full-Window Averages：

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M4 = movmean(A, 4, 'Endpoints', 'discard');

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M4 =
    4.2500    2.7500         0   -1.7500   -0.7500    0.7500    2.7500

image-20220925231334507

Trailing Moving Average of Vector

Example 1: movmean(A, [2, 1])

M = movmean(A,[kb kf]) computes the mean with a window of length kb+kf+1 that includes the element in the current position, kb elements backward, and kf elements forward.这种情况可以将使滑动平均不包含“未来值”。

如：

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M5 = movmean(A, [2, 1]);

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M5 =
    6.0000    6.0000    4.2500    2.7500         0   -1.7500   -0.7500    0.7500    2.7500    4.0000

image-20220926124803586

Example 2: movmean(A, [2, 1], 'Endpoints', 'discard')

同样地，只计算Full-Window Averages：

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M6 = movmean(A, [2, 1], 'Endpoints', 'discard');

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M6 =
    4.2500    2.7500         0   -1.7500   -0.7500    0.7500    2.7500

image-20220925233158393

Example 3: movmean(A, [2, 0])

如果只由“过去值”计算均值：

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M7 = movmean(A, [2, 0]);

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M7 =
    4.0000    6.0000    6.0000    4.3333    1.0000   -2.0000   -2.0000   -0.3333    2.0000    4.0000

image-20220926124906435

Example 4: movmean(A, [2, 0], 'Endpoints', 'discard')

同样地，如果只计算Full-Window Averages：

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M8 = movmean(A, [2, 0], 'Endpoints', 'discard');

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M8 =
    6.0000    4.3333    1.0000   -2.0000   -2.0000   -0.3333    2.0000    4.0000

image-20220925233522871


参考

[1] movmean - MathWorks.

[2] movmedian - MathWork.