Skip to main content
`Ctrl`+`K`
scipy.signal.

# cspline1d

scipy.signal.cspline1d(signal, lamb=0.0)

  Compute cubic spline coefficients for rank-1 array.

  Find the cubic spline coefficients for a 1-D signal assuming mirror-symmetric boundary conditions. To obtain the signal back from the spline representation mirror-symmetric-convolve these coefficients with a length 3 FIR window [1.0, 4.0, 1.0]/ 6.0 .

  Parameters:
    signal ndarray

      A rank-1 array representing samples of a signal.

    lamb float, optional

      Smoothing coefficient, default is 0.0.

  Returns:
    c ndarray

      Cubic spline coefficients.

  See also

  `cspline1d_eval`

    Evaluate a cubic spline at the new set of points.

  Notes

  Array API Standard Support

  `cspline1d` 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 | ⚠️ no JIT | ⛔
  Dask | ⚠️ computes graph | n/a

  See Support for the array API standard for more information.

  Examples

  We can filter a signal to reduce and smooth out high-frequency noise with a cubic spline:

      >>> import numpy as np
      >>> import matplotlib.pyplot as plt
      >>> from scipy.signal import cspline1d, cspline1d_eval
      >>> rng = np.random.default_rng()
      >>> sig = np.repeat([0., 1., 0.], 100)
      >>> sig += rng.standard_normal(len(sig))*0.05  # add noise
      >>> time = np.linspace(0, len(sig))
      >>> filtered = cspline1d_eval(cspline1d(sig), time)
      >>> plt.plot(sig, label="signal")
      >>> plt.plot(time, filtered, label="filtered")
      >>> plt.legend()
      >>> plt.show()