Time for action – interpolating in one dimension

We will create data points using a sinc() function and add some random noise to it. After this, we will do a linear and cubic interpolation and plot the results.

1. Create the data points and add noise to it:

   x = np.linspace(-18, 18, 36)
   noise = 0.1 * np.random.random(len(x))
   signal = np.sinc(x) + noise

2. Create a linear interpolation function and apply it to an input array with five times as many data points:

   interpreted = interpolate.interp1d(x, signal)
   x2 = np.linspace(-18, 18, 180)
   y = interpreted(x2)

3. Do the same as in the previous step, but with cubic interpolation:

   cubic = interpolate.interp1d(x, signal, kind="cubic")
   y2 = cubic(x2)

4. Plot the results with matplotlib:

   plt.plot(x, signal, 'o', label="data")
   plt.plot(x2, y, '-', label="linear")
   plt.plot(x2, y2, '-', lw=2, label="cubic")
   plt.legend()
   plt.show()

   The following diagram is a plot of the data, linear, and cubic interpolation...