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 on the original time series to extract the fast variations. These are just two common examples among a wide variety of applications of linear filters.

Getting ready

Download the Nasdaq dataset from the book's GitHub repository at https://github.com/ipython-books/cookbook-data and extract it in the current directory.

The data has been obtained from http://finance.yahoo.com/q/hp?s=^IXIC&a=00&b=1&c=1990&d=00&e=1&f=2014&g=d.

How to do it...

1. Let's import the packages:

   In [1]: import numpy as np
           import scipy as sp
           import scipy.signal as sg
   ...