Optimally Smoothing Noisy Curves

Consider a dataset approximated by:

import numpy as np
x = np.linspace(0, 2*np.pi, 100)
y = np.sin(x)   np.random.random(100) * 0.2

This includes 20% variation. Approaches like UnivariateSpline and moving averages present limitations.

Savitzky-Golay Filter

An effective solution is the Savitzky-Golay filter, available in scipy. It uses least squares regression to estimate the value at the center of a small window using a polynomial. The window then shifts to repeat the process, resulting in optimized adjustment of each point.

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()