Plotting a Fast Fourier Transform in Python

Question

I have access to numpy and scipy and want to create a simple FFT of a dataset. I have two lists one that is y values and the other is timestamps for those y values.

What is the simplest way to feed these lists into a scipy or numpy method and plot the resulting FFT?

I have looked up examples, but they all rely on creating a set of fake data with some certain number of data points, and frequency, etc. and doesn't really show how to do it with just a set of data and the corresponding timestamps.

I have tried the following example:

from scipy.fftpack import fft 

# Number of samplepoints 

N = 600 

# sample spacing 

T = 1.0 / 800.0 

x = np.linspace(0.0, N*T, N) 

y = np.sin(50.0 * 2.0*np.pi*x) + 0.5*np.sin(80.0 * 2.0*np.pi*x) 

yf = fft(y) 

xf = np.linspace(0.0, 1.0/(2.0*T), N/2) 

import matplotlib.pyplot as plt 

plt.plot(xf, 2.0/N * np.abs(yf[0:N/2]))

 plt.grid() 

plt.show()

But when I change the argument of fft to my data set and plot it I get extremely odd results, it appears the scaling for the frequency may be off. I am unsure.

Here is a Pastebin of the data I am attempting to FFT

http://pastebin.com/0WhjjMkb http://pastebin.com/ksM4FvZS

When i do an fft on the whole thing it just has a huge spike at zero and nothing else

Here is my code:

## Perform FFT WITH SCIPY 

signalFFT = fft(yInterp) 

## Get Power Spectral Density

signalPSD = np.abs(signalFFT) ** 2 

## Get frequencies corresponding to signal PSD 

fftFreq = fftfreq(len(signalPSD), spacing) 

## Get positive half of frequencies 

i = fftfreq>0 

## 

plt.figurefigsize=(8,4)); 

plt.plot(fftFreq[i], 10*np.log10(signalPSD[i])); 

#

plt.xlim(0, 100); 

plt.xlabel('Frequency Hz'); 

plt.ylabel('PSD (dB)')

spacing is just equal to xInterp[1]-xInterp[0]

Answer 1

You can plot the fast furier transform in Python you can run a functionally equivalent form of your code in an IPython notebook:

%matplotlib inline 

import numpy as np 

import matplotlib.pyplot as plt 

import scipy.fftpack 

# Number of samplepoints 

N = 600 

# sample spacing 

T = 1.0 / 800.0 

x = np.linspace(0.0, N*T, N) 

y = np.sin(50.0 * 2.0*np.pi*x) + 0.5*np.sin(80.0 * 2.0*np.pi*x)

yf = scipy.fftpack.fft(y) 

xf = np.linspace(0.0, 1.0/(2.0*T), N/2) fig, 

ax = plt.subplots() 

ax.plot(xf, 2.0/N * np.abs(yf[:N//2])) 

plt.show()

To know more about this you can have a look at the following video tutorial:-

If you wish to learn more about Python, visit the Python tutorial and Python course by Intellipaat.