Created
May 22, 2022 15:45
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Savitzky–Golay filter example
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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() |
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