Interpolation for smoothing data in SciPy

Introduction

Interpolation helps fill in missing points or smooth out noisy data by estimating values between known data points.

You have a few measurements and want to estimate values in between.

Your data is noisy and you want a smooth curve to see trends clearly.

You want to create a smooth line for a graph from scattered points.

You need to predict values at points where you did not measure.

Syntax

SciPy

from scipy.interpolate import interp1d

f = interp1d(x, y, kind='linear')
y_new = f(x_new)

x and y are your original data points.

kind can be 'linear', 'cubic', or others to control smoothness.

Examples

Linear interpolation estimates the value at 1.5 between points (1,1) and (2,4).

SciPy

from scipy.interpolate import interp1d

x = [0, 1, 2]
y = [0, 1, 4]
f = interp1d(x, y, kind='linear')
y_new = f(1.5)

Cubic interpolation gives a smoother curve estimate at 1.5 using more points.

SciPy

from scipy.interpolate import interp1d

x = [0, 1, 2, 3]
y = [0, 1, 4, 9]
f = interp1d(x, y, kind='cubic')
y_new = f(1.5)

Sample Program

This program shows how linear and cubic interpolation create smooth curves from noisy data points.

SciPy

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d

# Original data points
x = np.array([0, 1, 2, 3, 4, 5])
y = np.array([0, 0.8, 0.9, 0.1, -0.8, -1])

# Create interpolation functions
f_linear = interp1d(x, y, kind='linear')
f_cubic = interp1d(x, y, kind='cubic')

# New x values for smooth curve
x_new = np.linspace(0, 5, 50)

# Interpolated y values
y_linear = f_linear(x_new)
y_cubic = f_cubic(x_new)

# Plot original points and interpolations
plt.scatter(x, y, label='Original data')
plt.plot(x_new, y_linear, label='Linear interpolation')
plt.plot(x_new, y_cubic, label='Cubic interpolation')
plt.legend()
plt.title('Interpolation for smoothing data')
plt.show()

Important Notes

Interpolation only estimates between known points; it does not predict beyond the data range unless you allow extrapolation.

Cubic interpolation is smoother but needs at least 4 points.

Summary

Interpolation fills gaps between data points to create smooth curves.

Use interp1d from SciPy with different kind options for smoothness.

Visualizing interpolation helps understand data trends better.