[FIXED] savgol_filter from scipy.signal library, get the resulting polinormial function?

Issue

savgol_filter gives me the series.

I want to get the underlying polynormial function.
The function of the red line in a below picture.
So that I can extrapolate a point beyond the given x range.
Or I can find the slope of the function at the two extreme data points.

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import savgol_filter

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

plt.plot(x,y)

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

Solution

** edit** Since the filter uses least squares regression to fit the data in a small window to a polynomial of given degree, you can probably only extrapolate from the ends. I think the fitted curve is a piecewise function of these 'fits' and each function would not be a good representation of the entire data as a whole. What you could do is take the end windows of your data, and fit them to the same polynomial degree as the savitzy golay filter (using scipy's polyfit). It likely will not be accurate very far from the window though.

You can also use scipy.signal.savgol_coeffs() to get the coefficients of the filter. I think you dot product the coefficient array with your array of data to get the value at each point. You can include a derivative argument to get the slope at the ends of your data.

https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.savgol_coeffs.html#scipy.signal.savgol_coeffs

Answered By - Joe