gauss_spline(x, n)

Notes

The B-spline basis function can be approximated well by a zero-mean Gaussian function with standard-deviation equal to $\sigma=(n+1)/12$ for large n :

$$\frac{1}{\sqrt {2\pi\sigma^2}}exp(-\frac{x^2}{2\sigma})$$

Parameters

x : array_like

a knot vector

n : int

The order of the spline. Must be non-negative, i.e., n >= 0

Returns

res : ndarray

B-spline basis function values approximated by a zero-mean Gaussian function.

Gaussian approximation to B-spline basis function of order n.

Examples

We can calculate B-Spline basis functions approximated by a gaussian distribution:

>>> from scipy.signal import gauss_spline, bspline
... knots = np.array([-1.0, 0.0, -1.0])
... gauss_spline(knots, 3)
array([0.15418033, 0.6909883, 0.15418033])  # may vary

>>> bspline(knots, 3)
array([0.16666667, 0.66666667, 0.16666667])  # may vary

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.signal._bsplines.gauss_spline

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