Remove polynomial trend

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Syntax

D = detrend(A)

D = detrend(A,n)

D = detrend(A,n,bp)

D = detrend(___,nanflag)

D = detrend(___,Name,Value)

Description

example

D = detrend(A) removes the best straight-fit line from the data in A and returns the remaining data.

If A is a vector, then detrend subtracts the trend from the elements of A.
If A is a matrix, then detrend operates on each column separately, subtracting each trend from the corresponding column of A.
If A is a multidimensional array, then detrend operates column-wise across all dimensions, subtracting each trend from the corresponding column of A.
If A is a table or timetable with numeric variables of type single or double, then detrend operates on each variable of A separately, subtracting each trend from the corresponding variable of A.

You can use detrend functionality interactively by adding the Find and Remove Trends task to a live script.

example

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

example

D = detrend(A,n,bp) removes a continuous, piecewise trend with segments defined by the breakpoints specified in the vector bp.

D = detrend(___,nanflag) specifies whether to include or omit NaN values in A for any of the previous syntaxes. For example, detrend(A,"omitnan") ignores NaN values when computing the trend. By default, detrend includes NaN values.

example

D = detrend(___,Name,Value) specifies additional parameters using one or more name-value arguments. For example, detrend(A,1,bp,"Continuous",false) specifies that the fitted trend can have discontinuities.

Examples

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Continuous Linear Trend

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;A = 3*sin(t) + t;D = detrend(A);plot(t,A)hold onplot(t,D)plot(t,A-D,":k")legend("Input Data","Detrended Data","Trend")

Continuous Quadratic Trend

Open Live Script

Discontinuous Linear Trend

Open Live Script

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

t = -10:10;A = t.^3 + 6*t.^2 + 4*t + 3;bp = 0;D = detrend(A,1,bp,"SamplePoints",t,"Continuous",false);plot(t,A)hold onplot(t,D)plot(t,A-D,":k")legend("Input Data","Detrended Data","Trend","Location","northwest")

Input Arguments

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`A` — Input data
vector | matrix | multidimensional array | table | timetable

Input data, specified as a vector, matrix, multidimensional array, table, or timetable.

If A is a vector, then detrend subtracts the trend from the elements of A.
If A is a matrix, then detrend operates on each column separately, subtracting each trend from the corresponding column of A.
If A is a multidimensional array, then detrend operates column-wise across all dimensions, subtracting each trend from the corresponding column of A.
If A is a table or timetable with numeric variables of type single or double, then detrend operates on each variable of A separately, subtracting each trend from the corresponding variable of A.

Data Types: double | single
Complex Number Support: Yes

`n` — Polynomial degree
nonnegative integer scalar | `"constant"` | `"linear"`

Polynomial degree, specified as a nonnegative integer scalar, or as "constant" (equivalent to 0) or "linear" (equivalent to 1).

`bp` — Breakpoints
vector

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

Sample point values indicating the location of the breakpoints. Sample point values are contained either in the default sample points vector [1 2 3 ...] or specified by the SamplePoints name-value argument.
Logical values where logical 1 (true) indicates a breakpoint in the corresponding element of the input data. If bp contains logical values, it must be the same length as the sample points.

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

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

`nanflag` — Missing value condition
`"includemissing"` (default) | `"includenan"` | `"omitmissing"` | `"omitnan"`

Missing value condition, specified as one of these values:

"includemissing" or "includenan" — Include NaN values in A when computing the trend. If any element in the operating dimension is NaN, then the corresponding elements in D are NaN. "includemissing" and "includenan" have the same behavior.
"omitmissing" or "omitnan" — Ignore NaN values in A when computing the trend. If all elements in the operating dimension are NaN, then the corresponding elements in D are NaN. "omitmissing" and "omitnan" have the same behavior.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: D = detrend(A,SamplePoints=1:10:1000)

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: D = detrend(A,"SamplePoints",1:10:1000)

`Continuous` — Continuity constraint
`true` (default) | `false`

Continuity constraint, specified as one of these values:

true — The fitted trend must be continuous everywhere.
false — The fitted trend can contain discontinuities.

`SamplePoints` — Sample points
vector | table variable name | scalar | function handle | table `vartype` subscript

Sample points, specified as a vector of sample point values or one of the options in the following table when the input data is a table. The sample points represent the x-axis locations of the data, and must be sorted and contain unique elements. Sample points do not need to be uniformly sampled. The vector [1 2 3 ...] is the default.

When the input data is a table, you can specify the sample points as a table variable using one of these options:

Indexing Scheme	Examples
Variable name: A string scalar or character vector	`"A"` or `'A'` — A variable named `A`
Variable index: An index number that refers to the location of a variable in the table A logical vector. Typically, this vector is the same length as the number of variables, but you can omit trailing `0` or `false` values	`3` — The third variable from the table `[false false true]` — The third variable
Function handle: A function handle that takes a table variable as input and returns a logical scalar	`@isnumeric` — One variable containing numeric values
Variable type: A vartype subscript that selects one variable of a specified type	`vartype("numeric")` — One variable containing numeric values

Note

This name-value argument is not supported when the input data is a timetable. Timetables use the vector of row times as the sample points. To use different sample points, you must edit the timetable so that the row times contain the desired sample points.

Example: detrend(A,"SamplePoints",0:0.1:10)

Data Types: double | single | datetime | duration

`DataVariables` — Table or timetable variables to operate on
table variable name | timetable variable name | scalar | vector | cell array | pattern | function handle | table `vartype` subscript

Table or timetable variables to operate on, specified as one of the options in this table. The DataVariables value indicates for which variables of the input table or timetable to remove polynomial trends.

Other variables in the table or timetable not specified by DataVariables pass through to the output without being detrended.

Indexing Scheme	Examples
Variable names: A string or character vector A string array or cell array of character vectors A `pattern` object	`"A"` or `'A'` — A variable named `A` `["A" "B"]` or `{'A','B'}` — Two variables named `A` and `B` `"Var"+digitsPattern(1)` — Variables named `"Var"` followed by a single digit
Variable index: An index number that refers to the location of a variable in the table A vector of numbers A logical vector. Typically, this vector is the same length as the number of variables, but you can omit trailing `0` or `false` values.	`3` — The third variable from the table `[2 3]` — The second and third variables from the table `[false false true]` — The third variable
Function handle: A function handle that takes a table variable as input and returns a logical scalar	`@isnumeric` — All the variables containing numeric values
Variable type: A vartype subscript that selects variables of a specified type	`vartype("numeric")` — All the variables containing numeric values

For vector, matrix, or multidimensional array input data, DataVariables is not supported.

Example: detrend(A,"DataVariables",["Var1" "Var2" "Var4"])

`ReplaceValues` — Replace values indicator
`true` or `1` (default) | `false` or `0`

Replace values indicator, specified as one of these values when A is a table or timetable:

true or 1 — Replace input table variables with table variables containing detrended data.
false or 0 — Append input table variables with table variables containing detrended data.

For vector, matrix, or multidimensional array input data, ReplaceValues is not supported.

Example: detrend(A,"ReplaceValues",false)

Tips

The detrend function subtracts the mean or a best-fit line (in the least-squares sense) from your data. If your data is tabular or contains several data columns or is a table or timetable, detrend treats each data column separately.
Removing a trend from the data enables you to focus your analysis on the fluctuations in the data about the trend. A linear trend typically indicates a systematic increase or decrease in the data. A systematic shift can result from sensor drift, for example. While trends can be meaningful, some types of analyses yield better insight once you remove trends.
Whether it makes sense to remove trend effects in the data often depends on the objectives of your analysis.

Alternative Functionality

Live Editor Task

You can use detrend functionality interactively by adding the Find and Remove Trends task to a live script.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

If the input argument bp is supplied but not logical, the argument must be sorted in ascending order.
If the input argument bp is supplied but variable-sizing disabled, the argument must contain integers in the interval [1,m-2]. In this case, m is the number of elements in a column of the input argument A or the number of elements in A when A is a row vector (m = length(A)).
If the SamplePoints name-value argument is specified, variable-sizing is required.
If polynomial degree n is neither a constant nor a logical, variable-sizing is required.
Code generation uses a different method than MATLAB^® to detect nonunique or ill-conditioned problems to issue warnings. The code generation warnings do not always match the MATLAB warnings.
The function detrend does not use rand in code generation.
Code generation for detrending table or timetable variables is not supported.

Thread-Based Environment
Run code in the background using MATLAB® `backgroundPool` or accelerate code with Parallel Computing Toolbox™ `ThreadPool`.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

GPU arrays as table or timetable variables are not supported.

Version History

Introduced before R2006a

expand all

R2023a: Specify missing value condition

Include or omit missing values in the input array when computing the trend by using the "includemissing" or "omitmissing" options. These options have the same behavior as the "includenan" and "omitnan" options, respectively.

R2022b: Detrend tabular data

When detrending table or timetable data, you can:

Specify tabular variables to detrend by using the DataVariables name-value argument.
Append or replace tabular variables with variables containing detrended data by using the ReplaceValues name-value argument.
Specify the sample points as a table variable by using the SamplePoints name-value argument. SamplePoints is not supported when the input data is a timetable.

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Remove polynomial trend - MATLAB detrend (2024)

FAQs

How do you remove a polynomial trend in Matlab? ›

You can use detrend functionality interactively by adding the Find and Remove Trends task to a live script. D = detrend( A , n ) removes the n th-degree polynomial trend. For example, when n = 0 , detrend removes the mean value from A .

Read On ›

How do you remove trends from data in Matlab? ›

To eliminate the linear trend, use the MATLAB® function detrend . dt_ecgl = detrend(ecgl); To eliminate the nonlinear trend, fit a low-order polynomial to the signal and subtract it. In this case, the polynomial is of order 6.

How can one remove the trend from a time series process by detrending method? ›

So, to detrend a time series, we need to estimate the trend component and then subtract it from the original data, leaving us with only the seasonal component and the noise.

Show Me More ›

What is the alternative to detrending in Matlab? ›

As an alternative to detrending data beforehand, you can specify the offsets levels as estimation options and use them directly with the estimation command. The advantage of this approach is that there is a record of offset levels in the model in model.

Get More Info ›

How to use detrend function in MATLAB? ›

data_d = detrend( data ) computes and subtracts the mean value from each time-domain signal in data . The iddata objects data_d and data each contain input and output data originating from SISO, MIMO, or multiexperiment datasets. data_d = detrend( data , Type ) subtracts the trend you specify in Type .

Explore More ›

How do you reduce polynomials in MATLAB? ›

r = polynomialReduce( p , d ) returns the Polynomial Reduction of p by d with respect to all variables in p determined by symvar . The input d can be a vector of polynomials. r = polynomialReduce( p , d , vars ) uses the polynomial variables in vars .

Get More Info Here ›

How does differencing remove trend? ›

For example, first-differencing a time series will remove a linear trend (i.e., differences = 1 ); twice-differencing will remove a quadratic trend (i.e., differences = 2 ). In addition, first-differencing a time series at a lag equal to the period will remove a seasonal trend (e.g., set lag = 12 for monthly data).

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How do you remove a trend from a signal? ›

A very simple method to remove the trend in a signal is to know the trend a priori and to subtract this value. If the application allows for a so-called pre-measurement, it is rather simple to obtain an estimate for the mean of the signal (with or without the desired signal component).

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How to remove a pattern from a string in MATLAB? ›

newStr = erase( str , match ) deletes all occurrences of match in str . The erase function returns the remaining text as newStr . If match is an array, then erase deletes every occurrence of every element of match in str . The str and match arguments do not need to be the same size.

See Details ›

What are the two methods of eliminating trend in a time series? ›

1. Fit a trend line to the data, using least squares regression. 2. Detrend the data by subtracting the trend component from the data (additive model).

Read The Full Story ›

What is the difference between time series and detrend? ›

Detrending shows a different aspect of time series data by removing deterministic and stochastic trends. One of the most common uses of detrending is in a data set that shows some kind of overall increase.

Discover More ›

Why is it necessary to detrend or flatten data before seasonality analysis? ›

For example, a detrended dataset may be necessary to see a more accurate account of a company's sales in a given year more clearly by shifting the entire dataset from a slope to a flat surface to better expose the underlying cycles and fluctuations.

Read On ›

What is the detrend constant in MATLAB? ›

y = detrend(x, 'constant' ) removes the mean value from vector x or, if x is a matrix, from each column of the matrix. y = detrend(x, 'linear',bp ) removes a continuous, piecewise linear trend from vector x or, if x is a matrix, from each column of the matrix.

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What is iddata in MATLAB? ›

The iddata object stores time-domain data or frequency-domain data and has several properties that specify the time or frequency values. To modify the time or frequency values, you must change the corresponding property values.

Tell Me More ›

What is the equation for detrend? ›

We calculate the detrended time series ˆxt=xt−Tt. We model the seasonality St of the detrended time series {ˆxt}. We calculate the detrended and seasonally adjusted time series ˆˆxt =ˆxt−St.

Find Out More ›

How do you undo changes in MATLAB? ›

Alternatively, use the keyboard shortcuts for Undo and Redo. The shortcuts are defined in your MATLAB^® preferences. On a Windows^® platform, the default keyboard shortcuts for Undo and Redo are Ctrl+Z and Ctrl+Y. Each undo operation reverts the last change.

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How do you remove harmonics in MATLAB? ›

Filter Settings

Specifically, nf + bw/2 must fall within [0 F_s/2]. Here, n is the number of harmonics, f is the fundamental target frequency, and bw is the notch bandwidth. Fundamental frequency — Choose the fundamental frequency based on your knowledge of the lowest harmonic frequency that you want to remove.

Remove polynomial trend - MATLAB detrend (2024)

Syntax

Description