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11.9.1. astroML.filters.savitzky_golay

astroML.filters.savitzky_golay(y, window_size, order, deriv=0, use_fft=True)[source]

Smooth (and optionally differentiate) data with a Savitzky-Golay filter

This implementation is based on [R16].

The Savitzky-Golay filter removes high frequency noise from data. It has the advantage of preserving the original shape and features of the signal better than other types of filtering approaches, such as moving averages techhniques.

Parameters :

y : array_like, shape (N,)

the values of the time history of the signal.

window_size : int

the length of the window. Must be an odd integer number.

order : int

the order of the polynomial used in the filtering. Must be less then window_size - 1.

deriv: int :

the order of the derivative to compute (default = 0 means only smoothing)

use_fft : bool

if True (default) then convolue using FFT for speed

Returns :

y_smooth : ndarray, shape (N)

the smoothed signal (or it’s n-th derivative).

Notes

The Savitzky-Golay is a type of low-pass filter, particularly suited for smoothing noisy data. The main idea behind this approach is to make for each point a least-square fit with a polynomial of high order over a odd-sized window centered at the point.

References

[R16](1, 2) http://www.scipy.org/Cookbook/SavitzkyGolay
[R17]A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8), pp 1627-1639.
[R18]Numerical Recipes 3rd Edition: The Art of Scientific Computing W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery Cambridge University Press ISBN-13: 9780521880688

Examples

>>> t = np.linspace(-4, 4, 500)
>>> y = np.exp(-t ** 2)
>>> np.random.seed(0)
>>> y_noisy = y + np.random.normal(0, 0.05, t.shape)
>>> y_smooth = savitzky_golay(y, window_size=31, order=4)
>>> print np.rms(y_noisy - y)
>>> print np.rms(y_smooth - y)