# Detrend

Remove linear trend from vectors

Libraries:
DSP System Toolbox / Statistics

## Description

The Detrend block removes a linear trend from the length-M input vector, u, by subtracting the straight line that best fits the data in the least squares sense.

The least squares line, û = ax + b, is the line with parameters a and b that minimizes the quantity

$\sum _{i=1}^{M}{\left({u}_{i}-{\stackrel{^}{u}}_{i}\right)}^{2}$

for M evenly-spaced values of x, where ui is the ith element in the input vector. The output, y = u-û, is always an M-by-1 column vector.

## Ports

### Input

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Input data, specified as a vector. The block removes the straight line that best fits the data in the least squares sense.

Data Types: single | double

### Output

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Output data, returned as a column vector. The block returns the remaining data after removing the straight line that best fits the data in the least squares sense.

Data Types: single | double

## Block Characteristics

 Data Types double | single Multidimensional Signals No Variable-Size Signals No

## Version History

Introduced before R2006a