scipy.signal.savgol_coeffs

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

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). window_length must be an odd positive integer.

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

New 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.

Examples

>>> 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])

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