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.
Examples
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