Savitzky–Golay filter example

example.py

import numpy as np
import matplotlib.pyplot as plt

def savitzky_golay(y, window_size, order, deriv=0, rate=1):

    from math import factorial    
    try:
        window_size = np.abs(np.int(window_size))
        order = np.abs(np.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
    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] * rate**deriv * factorial(deriv)
    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[::-1], y, mode='valid')

x = np.linspace(0,2*np.pi,100)
y = np.sin(x) + np.random.random(100) * 0.2
yhat = savitzky_golay(y, 51, 3) # window size 51, polynomial order 3

plt.plot(x,y)
plt.plot(x,yhat, color='red')
plt.show()