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 SavitzkyGolay filter
This implementation is based on [1].
The SavitzkyGolay 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
 yarray_like, shape (N,)
the values of the time history of the signal.
 window_sizeint
the length of the window. Must be an odd integer number.
 orderint
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_fftbool
if True (default) then convolue using FFT for speed
 Returns
 y_smoothndarray, shape (N)
the smoothed signal (or it’s nth derivative).
Notes
The SavitzkyGolay is a type of lowpass filter, particularly suited for smoothing noisy data. The main idea behind this approach is to make for each point a leastsquare fit with a polynomial of high order over a oddsized window centered at the point.
References
 1(1,2)
 2
A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8), pp 16271639.
 3
Numerical Recipes 3rd Edition: The Art of Scientific Computing W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery Cambridge University Press ISBN13: 9780521880688
Examples
>>> t = np.linspace(4, 4, 500) >>> y = np.exp(t ** 2) >>> y_smooth = savitzky_golay(y, window_size=31, order=4)