Smoothing Curves with Dataset Noise: A Practical Guide

Smoothing curves for noisy datasets is a common challenge in data analysis. To address this, consider a dataset with a 20% variation due to noise:

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

For this situation, the Savitzky-Golay filter is an effective choice. This filter works by fitting a polynomial to a window of data points and using the polynomial to estimate the value at the center of the window. The window is then shifted along the data, and the process repeats, resulting in a smoothed curve.

Here's how to implement the Savitzky-Golay filter in Python:

1. Import the necessary libraries:

import numpy as np
import matplotlib.pyplot as plt

2. Run the Savitzky-Golay filter on the data:

yhat = savgol_filter(y, 51, 3) # window size 51, polynomial order 3

3. Visualize the original data and the smoothed curve:

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

The resulting curve will be smoother than the original while still preserving the underlying signal.

Note: If you don't have the savgol_filter function available, you can install it using the following command:

pip install scipy