Signal processing (time series analysis) for scientific data analysis with Python: Part 4

Linear and non-linear detrending of a time series

Image by Altuna Akalin

Links to part 1, part 2 and part 3 of this series.

There could be different kind of trends in your data which you know are not related to the actual process of your concern and you want to get rid of it. We can broadly divide them into two classes: Linear trend and non-linear trend. Let’s see how to remove these trends.

Linear trend

Let’s first create a dataset that show an unwanted linear trend. Importing required libraries;

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

Now let’s put a few lines to keep the figure sizes constant throughout.

plt.rcParams["font.size"] = 16
plt.rcParams['figure.figsize'] = (20, 10)

Let’s create a dataset of 1000 time points. Here I use the cumulative sum, cumsum(), of 1000 random points from a normal distribution to make it look more like a real dataset. I am adding a linear increase to it from -50 to 50.

#create signal
n = 1000
signal1 = np.cumsum(np.random.randn(n)) + np.linspace(-50,50, n)