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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:
    dataarray_like

      The input data.

    axisint, 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.

    bparray_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_databool, optional

      If True, perform in place detrending and avoid a copy. Default is False

  Returns:
    retndarray

      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.

  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.