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Module « scipy.signal »

Fonction savgol_coeffs - module scipy.signal

Signature de la fonction savgol_coeffs

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

Description

help(scipy.signal.savgol_coeffs)

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.

Returns
-------
coeffs : 1-D ndarray
    The filter coefficients.

See Also
--------
savgol_filter

Notes
-----
.. versionadded:: 0.14.0

References
----------
A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of Data by
Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8),
pp 1627-1639.
Jianwen Luo, Kui Ying, and Jing Bai. 2005. Savitzky-Golay smoothing and
differentiation filter for even number data. Signal Process.
85, 7 (July 2005), 1429-1434.

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,  2.07548111e-16, -1.00000000e-01,
       -2.00000000e-01])

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

>>> savgol_coeffs(5, 2, pos=3)
array([ 0.25714286,  0.37142857,  0.34285714,  0.17142857, -0.14285714])
>>> 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)
6.0

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