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scipy.signal.

# detrend

scipy.signal.detrend(data, axis=-1, type='linear', bp=0, overwrite_data=False)

  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.

  See also

  `numpy.polynomial.polynomial.Polynomial.fit`

    Create least squares fit polynomial.

  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 Support for the array API standard for more information.

  Examples

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

      >>> 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 `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 `Polynomial` also allows fitting higher degree polynomials. Consult its documentation on how to extract the polynomial coefficients.