Plotting power spectrum in python

Question

I have an array with 301 values, which were gathered from a movie clip with 301 frames. This means 1 value from 1 frame. The movie clip is running at 30 fps, so is in fact 1

Answer 1

Numpy has a convenience function, np.fft.fftfreq to compute the frequencies associated with FFT components:

from __future__ import division
import numpy as np
import matplotlib.pyplot as plt

data = np.random.rand(301) - 0.5
ps = np.abs(np.fft.fft(data))**2

time_step = 1 / 30
freqs = np.fft.fftfreq(data.size, time_step)
idx = np.argsort(freqs)

plt.plot(freqs[idx], ps[idx])

Note that the largest frequency you see in your case is not 30 Hz, but

In [7]: max(freqs)
Out[7]: 14.950166112956811

You never see the sampling frequency in a power spectrum. If you had had an even number of samples, then you would have reached the Nyquist frequency, 15 Hz in your case (although numpy would have calculated it as -15).