[Python] `np.gradient` has high variance for non-uniform spacing

I encountered high variance in np.gradient for relatively smooth data.

Suppose we want to calculate dx/dt:

import numpy as np
import matplotlib.pyplot as plt
x = np.array([13.11149679, 13.2141427 , 13.37743691, 13.3934357 , 13.56163066,
13.60207566, 13.69304133])
t = np.array([0.73065159, 0.74012055, 0.75911018, 0.7607452 , 0.77811468,
0.78031837, 0.79046324])
x_grad = np.gradient(x, t)

plt.plot(t[1:], np.diff(x) / np.diff(t), 'xb', label="findiff")
plt.plot(t, x_grad, 'or', label = 'np.gradient')
plt.plot(t, x, '+g', label = "x")
plt.xlabel('t')
plt.ylabel('x')
plt.legend()
plt.show()




The noise in data seems to be amplified by a lot. How should we deal with this?

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