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# detrend

remove constant, linear or piecewise linear trend from a vector

### Syntax

y = detrend(x) y = detrend(x,flag) y = detrend(x,flag,bp)

### Arguments

- x
vector or matrix of real or complex numbers (the signal to treat)

- flag
a string equal to "linear" (or "l") for linear or piecewise linear treatment or "constant" (or "c") for constant treatment.

- bp
the breakpoints to provide if you want a piecewise linear treatment.

- y
output, the signal x with the trend removed from it.

### Description

This function removes the constant or linear or
piecewise linear trend from a vector `x`

. In general
this can be useful before a fourier analysis. If `x`

is
matrix this function removes the trend of each column of x.

When `flag`

= "constant" or "c" `detrend`

removes the constant trend
(simply the mean of the signal) and when `flag`

= "linear" or "l" the function
removes the linear trend. By adding a third argument `bp`

it is possible to
remove a continuous *piecewise linear* trend. Note that the "instants" of the signal
`x`

goes from 0 to m-1 (m = length(x) if x is a vector and m = size(x,1) in case
x is a matrix). So the breakpoints `bp(i)`

must be reals in *[0 m-1]*
(breakpoints outside are simply removed from `bp`

vector).

The trend is got by a least square fit of `x`

on the appropriate function space.

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