Analyzing the frequency components of a signal with a Fast Fourier Transform

In this recipe, we will show how to use a Fast Fourier Transform (FFT) to compute the spectral density of a signal. The spectrum represents the energy associated to frequencies (encoding periodic fluctuations in a signal). It is obtained with a Fourier transform, which is a frequency representation of a time-dependent signal. A signal can be transformed back and forth from one representation to the other with no information loss.

In this recipe, we will illustrate several aspects of the Fourier transform. We will apply this tool to weather data spanning 20 years in France obtained from the US National Climatic Data Center.

How to do it...

1. Let's import the packages, including scipy.fftpack, which includes many FFT- related routines:

   >>> import datetime
       import numpy as np
       import scipy as sp
       import scipy.fftpack
       import pandas as pd
       import matplotlib.pyplot as plt
       %matplotlib inline

2. We import...