`scipy.signal._spline_filters:gauss_spline`

source: build-install/usr/lib/python3.14/site-packages/scipy/signal/_spline_filters.py:87

Signature

def gauss_spline(x, n)

Summary

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

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.

Notes

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

\frac{1}{2 π σ ^{2}} e x p (- \frac{x ^{2}}{2 σ})

Examples

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

import numpy as np
from scipy.signal import gauss_spline
knots = np.array([-1.0, 0.0, -1.0])

✓

gauss_spline(knots, 3)

✗

array([0.15418033, 0.6909883 , 0.15418033])