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scipy.signal.

# savgol_coeffs

scipy.signal.savgol_coeffs(window_length, polyorder, deriv=0, delta=1.0, pos=None, use='conv', *, xp=None, device=None)

  Compute the coefficients for a 1-D Savitzky-Golay FIR filter.

  Parameters:
    window_length int

      The length of the filter window (i.e., the number of coefficients).

    polyorder int

      The order of the polynomial used to fit the samples. polyorder must be less than window_length.

    deriv int, optional

      The order of the derivative to compute. This must be a nonnegative integer. The default is 0, which means to filter the data without differentiating.

    delta float, optional

      The spacing of the samples to which the filter will be applied. This is only used if deriv > 0.

    pos int or None, optional

      If pos is not None, it specifies evaluation position within the window. The default is the middle of the window.

    use str, optional

      Either ‘conv’ or ‘dot’. This argument chooses the order of the coefficients. The default is ‘conv’, which means that the coefficients are ordered to be used in a convolution. With use=’dot’, the order is reversed, so the filter is applied by dotting the coefficients with the data set.

    xp array_namespace, optional

      Optional array namespace. Should be compatible with the array API standard, or supported by array-api-compat. Default: `numpy`

    device any

      optional device specification for output. Should match one of the supported device specifications in `xp`.

  Returns:
    coeffs 1-D ndarray

      The filter coefficients.

  See also

  `savgol_filter`

  Notes

  Added in version 0.14.0.

  Array API Standard Support

  `savgol_coeffs` 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 | ✅ | n/a

  See Support for the array API standard for more information.

  References

  A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8), pp 1627-1639. Jianwen Luo, Kui Ying, and Jing Bai. 2005. Savitzky-Golay smoothing and differentiation filter for even number data. Signal Process. 85, 7 (July 2005), 1429-1434.

  Examples

      >>> import numpy as np
      >>> from scipy.signal import savgol_coeffs
      >>> savgol_coeffs(5, 2)
      array([-0.08571429,  0.34285714,  0.48571429,  0.34285714, -0.08571429])
      >>> savgol_coeffs(5, 2, deriv=1)
      array([ 2.00000000e-01,  1.00000000e-01,  2.07548111e-16, -1.00000000e-01,
             -2.00000000e-01])

  Note that use=’dot’ simply reverses the coefficients.

      >>> savgol_coeffs(5, 2, pos=3)
      array([ 0.25714286,  0.37142857,  0.34285714,  0.17142857, -0.14285714])
      >>> savgol_coeffs(5, 2, pos=3, use='dot')
      array([-0.14285714,  0.17142857,  0.34285714,  0.37142857,  0.25714286])
      >>> savgol_coeffs(4, 2, pos=3, deriv=1, use='dot')
      array([0.45,  -0.85,  -0.65,  1.05])

  x contains data from the parabola x = t**2, sampled at t = -1, 0, 1, 2, 3. c holds the coefficients that will compute the derivative at the last position. When dotted with x the result should be 6.

      >>> x = np.array([1, 0, 1, 4, 9])
      >>> c = savgol_coeffs(5, 2, pos=4, deriv=1, use='dot')
      >>> c.dot(x)
      6.0