pythonfftcanopy

Bandwidth of an EEG signal

I'm trying to perform FFT of an EEG signal in Python, and then basing on the bandwidth determine whether it's alpha or beta signal. It looked fine, but the resulting plots are nothing like they should, the frequencies and magnitude values are not what I expected. Any help appreciated, here's the code:

from scipy.io import loadmat
import scipy
import numpy as np
from pylab import *
import matplotlib.pyplot as plt

eeg = loadmat("eeg_2013.mat");
eeg1=eeg['eeg1'][0]
eeg2=eeg['eeg2'][0]
fs = eeg['fs'][0][0]
fft1 = scipy.fft(eeg1)
f = np.linspace (fs,len(eeg1), len(eeg1), endpoint=False)
plt.figure(1)
plt.subplot(211)
plt.plot (f, abs (fft1))
plt.title ('Magnitude spectrum of the signal')
plt.xlabel ('Frequency (Hz)')
show()
plt.subplot(212)
fft2 = scipy.fft(eeg2)
f = np.linspace (fs,len(eeg2), len(eeg2), endpoint=False)
plt.plot (f, abs (fft2))
plt.title ('Magnitude spectrum of the signal')
plt.xlabel ('Frequency (Hz)')
show()

And the plots: img

Solution

  • If your sampling frequency is fs and you have N=len(eeg1) samples, then the fft procedure will, of course, return an array of N values. The first N/2 of them correspond to the frequency range 0..fs/2, the second half of the frequency corresponds to the mirrored frequency range -fs/2..0. For real input signals the mirrored half is just the complex conjugate of the positive half, so it can be disregarded in further analysis (but not in the inverse fft).

    So essentially, you should format

    f=linspace(0,N-1,N)*fs/N

    Edit: or even more simple with minimal changes to the inital code

    f = np.linspace (0,fs,len(eeg1), endpoint=False)

    so f ranges from 0 to just before fs and disregard the second half of the fft result in the output:

    plt.plot( f(0:N/2), abs( fft1(0:N/2) ) )

    Added: You can use fftshift to exchange both halves, then the correct frequency range is

    f = np.linspace (-fs/2,fs/2,len(eeg1), endpoint=False)