Applying a linear filter to a digital signal

Linear filters play a fundamental role in signal processing. With a linear filter, one can extract meaningful information from a digital signal.

In this recipe, we will show two examples using stock market data (the NASDAQ stock exchange). First, we will smooth out a very noisy signal with a low-pass filter to extract its slow variations. We will also apply a high-pass filter to the original time series to extract the fast variations. These are just two common examples among a wide variety of applications of linear filters.

How to do it...

1. Let's import the packages:

   >>> import numpy as np
       import scipy as sp
       import scipy.signal as sg
       import pandas as pd
       import matplotlib.pyplot as plt
       %matplotlib inline

2. We load the NASDAQ data (obtained from https://finance.yahoo.com/quote/%5EIXIC/history?period1=631148400&period2=1510786800&interval=1d&filter=history&frequency=1d) with pandas:

   >>> nasdaq_df = pd...