`scipy.signal._signaltools:detrend`

source: /scipy/signal/_signaltools.py :4178

Signature

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

Summary

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, allow in place detrending and avoid a copy. Default is False. In place modification applies only if type == 'linear' and data is of the floating point dtype float32, float64, complex64 or complex128.

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.

Array API Standard Support

detrend has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ⛔                   
JAX                   ✅                     ✅                   
Dask                  ⚠️ computes graph     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

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
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

✓

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

Aliases

scipy.signal.detrend