user3123955 - 6 months ago 164

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

So I 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()
```

I get what I believe to be very reasonable output.

It's been longer than I care to admit since I was in engineering school thinking about signal processing, but spikes at 50 and 80 are exactly what I would expect. So what's the issue?

The problem here is that you don't have periodic data. You should always inspect the data that you feed into *any* algorithm to make sure that it's appropriate.

```
import pandas
import matplotlib.pyplot as plt
#import seaborn
%matplotlib inline
# the OP's data
x = pandas.read_csv('http://pastebin.com/raw.php?i=ksM4FvZS', skiprows=2, header=None).values
y = pandas.read_csv('http://pastebin.com/raw.php?i=0WhjjMkb', skiprows=2, header=None).values
fig, ax = plt.subplots()
ax.plot(x, y)
```