spkit.total_variation

spkit.total_variation(x, normalise=False, method='npdiff', **kwargs)

Total Variation of a signal

$$\begin{array}{r}\begin{array}{c}TV(x)=\sum _n|x_{n+1}-x_n|\\ TV(x)=\sum |\frac{dx}{dt}|\end{array}\end{array}$$

Bounds

$$min\{max(x)-min(x)\}\ge TV(x)\ge (n-1)\times min\{max(x)-min(x)\}$$

where $n=length(x)$

Returns:

tv: float

• Total Variation of x

References

• wikipedia - https://en.wikipedia.org/wiki/Total_variation

Examples

#sp.total_variation
import numpy as np
import matplotlib.pyplot as plt
import spkit as sp
x1, fs = sp.data.optical_sample(sample=1)
x2, fs = sp.data.optical_sample(sample=2)
tv_x1 = sp.total_variation(x1,normalise=False)
tv_x2 = sp.total_variation(x2,normalise=False)
print(f'TV(x1) = {tv_x1}')
print(f'TV(x2) = {tv_x2}')