Ojtwist - 7 months ago 388

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 10 sec long

Now I would like to get the power spectrum of this "signal" ( with the right Axis). I tried:

`X = fft(S_[:,2]);`

pl.plot(abs(X))

pl.show()

I also tried:

`X = fft(S_[:,2]);`

pl.plot(abs(X)**2)

pl.show()

Though I don't think this is the real spectrum.

the signal:

The spectrum:

The power spectrum :

Can anyone provide some help with this ?

Answer

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 = 1.0 / 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).