detrend

Remove polynomial trend

Syntax

D = detrend(A)

D = detrend(A,n)

D = detrend(A,n,bp)

D = detrend(___,nanflag)

D = detrend(___,Name,Value)

Description

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.

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.

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.

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

Continuous Linear Trend

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 on
plot(t,D)
plot(t,A-D,":k")
legend("Input Data","Detrended Data","Trend")

Continuous Quadratic Trend

Create a table of data, and remove the continuous quadratic trend from a specified variable in the table. Plot the original data, the detrended data, and the trend.

t = (-4:4)';
trend = (t.^2 + 4*t + 3);
sig = [0 1 -2 1 0 1 -2 1 0]';
x = sig + trend;
T = table(t,trend,sig,x);
T = detrend(T,2,"DataVariables","x","SamplePoints","t","ReplaceValues",false)

T=9×5 table
    t     trend    sig    x     x_detrended
    __    _____    ___    __    ___________

    -4      3       0      3     -0.12121  
    -3      0       1      1       0.9697  
    -2     -1      -2     -3      -1.9654  
    -1      0       1      1       1.0736  
     0      3       0      3      0.08658  
     1      8       1      9       1.0736  
     2     15      -2     13      -1.9654  
     3     24       1     25       0.9697  
     4     35       0     35     -0.12121  

plot(T,"t","x")
hold on
plot(T,"t","x_detrended")
plot(T.t,T.x-T.x_detrended,":k")
legend("Input Data","Detrended Data","Trend","Location","northwest")

Discontinuous Linear Trend

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 on
plot(t,D)
plot(t,A-D,":k")
legend("Input Data","Detrended Data","Trend","Location","northwest")

Input Arguments

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	Values to Specify	Examples
Variable name	A string scalar 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 (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 first dimension of A is variable size at code generation time, A cannot be a row vector at run time. To avoid this error, specify the first dimension of A with a fixed size of 1 at code generation time.

• If the input argument bp is used and is not logical, the elements of the bp vector must be sorted in ascending order.

• If the input argument bp is used and variable sizing is disabled, the bp vector must contain integers in the interval [1,m-2].

  • If A is a row vector, then m is length(A).

  • Otherwise, m is length(A(:,1)).

• If the SamplePoints name-value argument is specified, variable sizing must be enabled.

• If polynomial degree n is neither a constant nor a logical value, variable sizing must be enabled.

• The code generator uses a different method than MATLAB^® to detect nonunique or ill-conditioned problems. Therefore, the warnings produced by the code generator do not always match the warnings produced by MATLAB.

• Code generation does not support the detrend function for tables or timetables.

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™.

The detrend function supports GPU array input with these usage notes and limitations:

• GPU arrays as table or timetable variables are not supported.

Version History

Introduced before R2006a

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.