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# detrend

Remove polynomial trend

## Syntax

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

## Description

example

````y = detrend(x)` removes the best straight-fit line from the data in `x`. If `x` is a vector, then `detrend` subtracts the trend from the elements of `x`.If `x` is a matrix, then `detrend` operates on each column separately, subtracting each trend from the corresponding column. ```

example

````y = detrend(x,n)` removes the `n`th-degree polynomial trend. For example, when ```n = 0```, `detrend` removes the mean value from `x`. When `n = 1`, `detrend` removes the linear trend, which is equivalent to the previous syntax. When `n = 2`, `detrend` removes the quadratic trend.```

example

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

example

````y = detrend(___,Name,Value)` specifies additional parameters for any of the previous syntaxes 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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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') ``` 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') ``` 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') ``` ## Input Arguments

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Input array, specified as a vector, matrix, or multidimensional array. When `x` is a multidimensional array, `detrend` operates column-wise across all dimensions.

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

Polynomial degree, specified as a non-negative integer scalar, or as `'constant'` (equivalent to `0`) or `'linear'` (equivalent to `1`).

Break points, 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. If `bp` contains logical values, it must be the same length as the sample points.

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

### Name-Value Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

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 the x-axis, and they must be unique and sorted.

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

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