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Module « scipy.signal »

Fonction detrend - module scipy.signal

Signature de la fonction detrend

def detrend(data: 'np.ndarray', axis: 'int' = -1, type: "Literal['linear', 'constant']" = 'linear', bp: 'ArrayLike | int' = 0, overwrite_data: 'bool' = False) -> 'np.ndarray' 

Description

help(scipy.signal.detrend)

Remove linear or constant trend along axis from data.

Parameters
----------
data : array_like
    The input data.
axis : int, optional
    The axis along which to detrend the data. By default this is the
    last axis (-1).
type : {'linear', 'constant'}, optional
    The type of detrending. If ``type == 'linear'`` (default),
    the result of a linear least-squares fit to `data` is subtracted
    from `data`.
    If ``type == 'constant'``, only the mean of `data` is subtracted.
bp : array_like of ints, optional
    A sequence of break points. If given, an individual linear fit is
    performed for each part of `data` between two break points.
    Break points are specified as indices into `data`. This parameter
    only has an effect when ``type == 'linear'``.
overwrite_data : bool, optional
    If True, perform in place detrending and avoid a copy. Default is False

Returns
-------
ret : ndarray
    The detrended input data.

Notes
-----
Detrending can be interpreted as subtracting a least squares fit polynomial:
Setting the parameter `type` to 'constant' corresponds to fitting a zeroth degree
polynomial, 'linear' to a first degree polynomial. Consult the example below.

See Also
--------
numpy.polynomial.polynomial.Polynomial.fit: Create least squares fit polynomial.


Examples
--------
The following example detrends the function :math:`x(t) = \sin(\pi t) + 1/4`:

>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> from scipy.signal import detrend
...
>>> t = np.linspace(-0.5, 0.5, 21)
>>> x = np.sin(np.pi*t) + 1/4
...
>>> x_d_const = detrend(x, type='constant')
>>> x_d_linear = detrend(x, type='linear')
...
>>> fig1, ax1 = plt.subplots()
>>> ax1.set_title(r"Detrending $x(t)=\sin(\pi t) + 1/4$")
>>> ax1.set(xlabel="t", ylabel="$x(t)$", xlim=(t[0], t[-1]))
>>> ax1.axhline(y=0, color='black', linewidth=.5)
>>> ax1.axvline(x=0, color='black', linewidth=.5)
>>> ax1.plot(t, x, 'C0.-',  label="No detrending")
>>> ax1.plot(t, x_d_const, 'C1x-', label="type='constant'")
>>> ax1.plot(t, x_d_linear, 'C2+-', label="type='linear'")
>>> ax1.legend()
>>> plt.show()

Alternatively, NumPy's `~numpy.polynomial.polynomial.Polynomial` can be used for
detrending as well:

>>> pp0 = np.polynomial.Polynomial.fit(t, x, deg=0)  # fit degree 0 polynomial
>>> np.allclose(x_d_const, x - pp0(t))  # compare with constant detrend
True
>>> pp1 = np.polynomial.Polynomial.fit(t, x, deg=1)  # fit degree 1 polynomial
>>> np.allclose(x_d_linear, x - pp1(t))  # compare with linear detrend
True

Note that `~numpy.polynomial.polynomial.Polynomial` also allows fitting higher
degree polynomials. Consult its documentation on how to extract the polynomial
coefficients.

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