How to Smooth Noisy Data Curves: A Comprehensive Guide and Solution

Smoothing Curves for Noisy Data: A Comprehensive Guide

When dealing with datasets that exhibit noise or irregularities, it becomes crucial to find effective techniques to smooth out these deviations and extract the underlying trend. This article delves into various approaches to achieve curve smoothing, addressing the specific challenge of handling noise.

Univariate Spline Function

The UnivariateSpline function from Scipy is a common option for curve smoothing. However, it may not always handle noise effectively, as it tends to overfit the data and introduce additional noise.

Moving Average

A moving average approach can also be employed, which involves calculating the average of a subset of data points and using this as the smoothed value. However, selecting an appropriate delay for the moving average is critical to avoid excessive smoothing or underfitting.

Savitzky-Golay Filter: A Robust Solution

The Savitzky-Golay filter emerges as a robust solution for smoothing noisy curves. It utilizes a least squares approach to fit a polynomial to a small window of data points. By shifting the window and repeating the process, each point is optimally adjusted relative to its neighbors.

Implementation with SciPy

To implement the Savitzky-Golay filter in Python, one can use the savitzky_golay() function provided by the cookbook example or the savgol_filter() function from the SciPy library. The following code demonstrates how to use the savgol_filter() function to smooth a noisy sinusoidal dataset:

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

# Generate noisy sinusoidal data
x = np.linspace(0,2*np.pi,100)
y = np.sin(x) + np.random.random(100) * 0.2

# Apply Savitzky-Golay filter
yhat = savgol_filter(y, 51, 3) # window size 51, polynomial order 3

# Plot original and smoothed data
plt.plot(x,y)
plt.plot(x,yhat, color='red')
plt.show()

By applying the Savitzky-Golay filter, the noisy sinusoid is effectively smoothed while preserving the overall trend. This demonstrates the filter's effectiveness in reducing noise and extracting the underlying signal.

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