SciPy

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_length : int

The length of the filter window (i.e. the number of coefficients). window_length must be an odd positive integer.

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

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.

Examples

>>> 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,   2.00607895e-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])

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 = array([1, 0, 1, 4, 9])
>>> c = savgol_coeffs(5, 2, pos=4, deriv=1, use='dot')
>>> c.dot(x)
6.0000000000000018

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