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detrend

Remove polynomial trend

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Syntax

y = detrend(x)
y = detrend(x,n)
y = detrend(x,n,bp)
y = detrend(___,nanflag)
y = detrend(___,Name,Value)

Description

example

y = detrend(x)removes the best straight-fit line from the data inx.

  • Ifxis a vector, thendetrendsubtracts the trend from the elements ofx.

  • Ifxis a matrix, thendetrendoperates on each column separately, subtracting each trend from the corresponding column ofx.

example

y = detrend(x,n)removes thenth-degree polynomial trend. For example, whenn = 0,detrendremoves the mean value fromx. Whenn = 1,detrendremoves the linear trend, which is equivalent to the previous syntax. Whenn = 2,detrendremoves the quadratic trend.

example

y = detrend(x,n,bp)removes a continuous, piecewise trend with segments defined by the break pointsbp.

y = detrend(___,nanflag)specifies howNaNvalues are treated for any of the previous syntaxes. For example,detrend(x,'omitnan')removesNaN值计算趋势之前,detrend(x,'includenan')includes them (default).

example

y = detrend(___,Name,Value)指定额外的参数rs using one or more name-value pairs. For example,detrend(x,1,bp,'Continuous',false)specifies that the fitted trend can have discontinuities.

Examples

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Open Live Script

Create a vector of data, and remove the continuous linear trend. Plot the original data, the detrended data, and the linear trend.

t = 0:20; x = 3*sin(t) + t; y = detrend(x); plot(t,x,t,y,t,x-y,':k') legend('Input Data','Detrended Data','Trend','Location','northwest')

Figure contains an axes object. The axes object contains 3 objects of type line. These objects represent Input Data, Detrended Data, Trend.

Open Live Script

Create a vector of data, and remove the continuous quadratic trend. Plot the original data, the detrended data, and the trend.

t = 0:20; x = 20*sin(t) + t.^2; y = detrend(x,2); plot(t,x,t,y,t,x-y,':k') legend('Input Data','Detrended Data','Trend','Location','northwest')

Figure contains an axes object. The axes object contains 3 objects of type line. These objects represent Input Data, Detrended Data, Trend.

Open Live Script

Create a vector of data, and remove the piecewise linear trend using a break point at 0. Specify that the resulting output can be discontinuous. Plot the original data, the detrended data, and the trend.

t = -10:10; x = t.^3 + 6*t.^2 + 4*t + 3; bp = 0; y = detrend(x,1,bp,'SamplePoints',t,'Continuous',false); plot(t,x,t,y,t,x-y,':k') legend('Input Data','Detrended Data','Trend','Location','northwest')

Figure contains an axes object. The axes object contains 3 objects of type line. These objects represent Input Data, Detrended Data, Trend.

Input Arguments

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Input array, specified as a vector, matrix, or multidimensional array. Whenxis a multidimensional array,detrendoperates column-wise across all dimensions.

Data Types:double|single
Complex Number Support:Yes

Polynomial degree, specified as a non-negative integer scalar, or as'constant'(equivalent to0) or'linear'(equivalent to1).

Break points to define piecewise segments of the data, specified as a vector containing one of the following:

  • Sample point values indicating the location of the break points. Sample point values are contained either in the default sample points vector[1 2 3 ...]or in the vector specified by the'SamplePoints'parameter.

  • Logical values where logical 1 (true) indicates a break point in the corresponding element of the input data. Ifbpcontains logical values, it must be the same length as the sample points.

Break points are useful when you want to compute separate trends for different segments of the data.

Data Types:double|single|datetime|duration|logical

NaNcondition, specified as one of the following values:

  • 'includenan'— IncludeNaNvalues in the input data when computing the trend.

  • 'omitnan'— Ignore allNaNvalues in the input when computing the trend.

Name-Value Arguments

Specify optional pairs of arguments asName1=Value1,...,NameN=ValueN,在那里Nameis the argument name andValueis the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and encloseNamein quotes.

Example:y = detrend(x,'SamplePoints',1:10:1000)

Continuity constraint, specified as the comma-separated pair consisting of'Continuous'and one of the following:

  • true— The fitted trend must be continuous everywhere.

  • false— The fitted trend can contain discontinuities.

Sample points, specified as the comma-separated pair consisting of'SamplePoints'and a vector. The sample points represent the locations of the input data on thex-axis, and they must be unique and sorted.

Data Types:double|single|datetime|duration

Extended Capabilities

Version History

Introduced before R2006a

See Also

Functions

Live Editor Tasks

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