detrend

Remove polynomial trend

Syntax

y = detrend(x)

y = detrend(x,n)

y = detrend(x,n,bp)

y = detrend(___,Name,Value)

Description

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.

y = detrend(x,n) removes the nth-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.

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

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

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;
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') 

Continuous Quadratic Trend

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') 

Discontinuous Linear Trend

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

x — Input array

vector | matrix | multidimensional array

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
Complex Number Support: Yes

n — Polynomial degree

non-negative integer scalar | 'constant' | 'linear'

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

bp — Break points

vector

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. If bp contains 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

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)

'Continuous' — Continuity constraint

true (default) | false

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.

'SamplePoints' — Sample points

[1 2 3 ...] (default) | vector

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

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 x or the number of elements in x when x is a row vector (m = length(x)).

• If 'SamplePoints' parameter values are supplied, 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.

GPU Arrays

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

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).