`scipy.signal._savitzky_golay:savgol_coeffs`

source: /scipy/signal/_savitzky_golay.py:11

Signature

def savgol_coeffs(window_length, polyorder, deriv = 0, delta = 1.0, pos = None, use = conv, *, xp = None, device = None)

Summary

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.

Notes

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 dev-arrayapi for more information.

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,  2.16125056e-16, -1.00000000e-01,
       -2.00000000e-01])

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

savgol_coeffs(5, 2, pos=3)
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)

✗

np.float64(6.00000000000001)

Aliases

scipy.signal.savgol_coeffs