In this article, I will show you how to use the Savitzky-Golay filter in Python and show you how it works. To understand the Savitzky–Golay filter, you should be familiar with the moving average and linear regression.

The Savitzky-Golay filter has two parameters: the window size and the degree of the polynomial.

The window size parameter specifies how many data points will be used to fit a polynomial regression function. The second parameter specifies the degree of the fitted polynomial function (if we choose 1 as the polynomial degree, we end up using a linear regression function).

In every window, a new polynomial is fitted, which gives us the effect of smoothing the input dataset.

Take a look at the following animation (Source: Wikipedia Author: Cdang, Licence: CC BY‑SA 3.0)

In every step, the window moves and a different part of the original dataset is used. Then, the local polynomial function is fitted to the data in the window, and a new data point is calculated using the polynomial function. After that, the window moves to the next part of the dataset, and the process repeats.

Python

Here is a dataset of Bitcoin prices during the days between 2019-07-19 and 2019-08-17.

1
2
3
4
bitcoin.plot()
plt.title('Bitcoin price: 2019-07-19 - 2019-08-17')
plt.xlabel('Day')
plt.ylabel('BTC price in USD')

I’m going to smooth the data in 5 days-long windows using a first-degree polynomial and a second-degree polynomial.

1
2
3
4
5
6
7
8
9
10
from scipy.signal import savgol_filter

smoothed_2dg = savgol_filter(btc, window_length = 5, polyorder = 2)
smoothed_2dg

smoothed_1dg = savgol_filter(btc, window_length = 5, polyorder = 1)
smoothed_1dg

bitcoin['smoothed_2dg'] = smoothed_2dg
bitcoin['smoothed_1dg'] = smoothed_1dg

When we plot the result, we see the original data, and the two smoothed time-series.

1
2
3
4
bitcoin.plot()
plt.title('Bitcoin price: 2019-07-19 - 2019-08-17')
plt.xlabel('Day')
plt.ylabel('BTC price in USD')