code: def savitzky_golay(y, window_size, order, deriv=0, use_fft=True):
      r"""Smooth (and optionally differentiate) data with a Savitzky-Golay filter
  
      This implementation is based on [1]_.
  
      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.
  
      Examples
      --------
      >>> t = np.linspace(-4, 4, 500)
      >>> y = np.exp(-t ** 2)
      >>> y_smooth = savitzky_golay(y, window_size=31, order=4)
  
      References
      ----------
      .. [1] http://www.scipy.org/Cookbook/SavitzkyGolay
      .. [2] A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of
         Data by Simplified Least Squares Procedures. Analytical
         Chemistry, 1964, 36 (8), pp 1627-1639.
      .. [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 ISBN-13: 9780521880688
      """
      try:
          window_size = np.abs(int(window_size))
          order = np.abs(int(order))
      except ValueError:
          raise ValueError(
              "window_size and order have to be of type int"
          )
  
      if window_size % 2 != 1 or window_size < 1:
          raise TypeError(
              "window_size size must be a positive odd number"
          )
  
      if window_size < order + 2:
          raise TypeError(
              "window_size is too small for the polynomials order"
          )
  
      order_range = range(order + 1)
  
      half_window = (window_size - 1) // 2
  
      # precompute coefficients
      b = np.array(
          [
              [k**i for i in order_range]
              for k in range(-half_window, half_window + 1)
          ]
      )
      m = np.linalg.pinv(b)[deriv]
  
      # pad the signal at the extremes with
      # values taken from the signal itself
      firstvals = y[0] - np.abs(y[1 : half_window + 1][::-1] - y[0])
      lastvals = y[-1] + np.abs(y[-half_window - 1 : -1][::-1] - y[-1])
  
      y = np.concatenate((firstvals, y, lastvals))
  
      if use_fft:
          return signal.fftconvolve(y, m, mode="valid")
      else:
          return np.convolve(y, m, mode="valid")
  
imports: import numpy
  from scipy import optimize, fftpack, signal
  from astroML.utils.decorators import deprecated
  from astroML.utils.exceptions import AstroMLDeprecationWarning
label_desc: Use image node_id 1 for calling a global function with example usage: savitzky_golay(y, window_size, order, deriv, use_fft) and returns: signal, np