`scipy.signal._spline_filters:qspline1d`

source: /scipy/signal/_spline_filters.py :358

Signature

def qspline1d ( signal , lamb = 0.0 )

Summary

Compute quadratic spline coefficients for rank-1 array.

Parameters

signal : ndarray: A rank-1 array representing samples of a signal.
lamb : float, optional: Smoothing coefficient (must be zero for now).

Returns

c : ndarray: Quadratic spline coefficients.

Notes

Find the quadratic 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, 6.0, 1.0]/ 8.0 .

Array API Standard Support

qspline1d 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 dev-arrayapi for more information.

Examples

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

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import qspline1d, qspline1d_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 = qspline1d_eval(qspline1d(sig), time)

✓

plt.plot(sig, label="signal")
plt.plot(time, filtered, label="filtered")
plt.legend()

✗

plt.show()

✓

Aliases

scipy.signal.qspline1d