scipy.signal.savgol_coeffs#

scipy.signal.savgol_coeffs(window_length, polyorder, deriv=0, delta=1.0, pos=None, use='conv')[source]#

Compute the coefficients for a 1-D Savitzky-Golay FIR filter.

Parameters:

window_lengthint: The length of the filter window (i.e., the number of coefficients).
polyorderint: The order of the polynomial used to fit the samples. polyorder must be less than window_length.
derivint, 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.
deltafloat, optional: The spacing of the samples to which the filter will be applied. This is only used if deriv > 0.
posint or None, optional: If pos is not None, it specifies evaluation position within the window. The default is the middle of the window.
usestr, 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:

coeffs1-D ndarray: The filter coefficients.

See also

savgol_filter

Notes

Added in version 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