[Numpy-discussion] Is Savitzky-Golay filter provided by cookbook different from matlab's?
Hexyl Chan
imhexyl at gmail.com
Sat Jan 15 04:15:07 EST 2011
I have used the Savitzky-Golay filter provided by cookbook, but the result
is different from the one given by matlab function sgolayfilt(x,2,15). I
attached the numpy code below:
#! /usr/bin/env python
# -*- coding:utf-8 -*-
import numpy as np
def savitzky_golay(y, window_size, order, deriv=0):
r"""Smooth (and optionally differentiate) data with a Savitzky-Golay
filter.
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)
Returns
-------
ys : 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 ) + np.random.normal(0, 0.05, t.shape)
ysg = savitzky_golay(y, window_size=31, order=4)
import matplotlib.pyplot as plt
plt.plot(t, y, label='Noisy signal')
plt.plot(t, np.exp(-t**2), 'k', lw=1.5, label='Original signal')
plt.plot(t, ysg, 'r', label='Filtered signal')
plt.legend()
plt.show()
References
----------
.. [1] A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of
Data by Simplified Least Squares Procedures. Analytical
Chemistry, 1964, 36 (8), pp 1627-1639.
.. [2] 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(np.int(window_size))
order = np.abs(np.int(order))
except ValueError, msg:
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.mat([[k**i for i in order_range] for k in range(-half_window,
half_window+1)])
m = np.linalg.pinv(b).A[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))
return np.convolve( m, y, mode='valid')
if __name__ == "__main__":
rrstype = np.dtype({'names':['wavelenth', 'rrs'], 'formats':['f','f']})
record_list = []
record_file = open("200607NO1.txt")
for line in record_file:
item_list = line.strip().split('\t')
record_list.append((item_list[0], item_list[1]))
record_file.close()
record_array = np.array(record_list,dtype=rrstype)
rrs_array = record_array["rrs"]
rrs_array_2 = savitzky_golay(rrs_array, 15, 2)
rrs_array_2.tofile("savitzky-golay-result.txt", "\n")
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