As Fourier coefficients are complex numbers, we can view magnitudes directly. Displaying magnitudes of Fourier transforms is called the spectrum of the transform. The value F [0,0] of the DFT is called the DC coefficient.

The DC coefficient is too large for the other coefficient values to be seen, which is why we need to stretch the transform values by displaying the logarithm of the transform. Also, for display convenience, the transform coefficients are shifted (with fftshift()) so that the DC component is in the center. Excited to create a Fourier spectrum of the rhino image? Code this:

# the quadrants are needed to be shifted around in order that the low spatial frequencies are in the center of the 2D fourier-transformed image.
freq2 = fp.fftshift(freq)
pylab.figure(figsize=(10,10)), pylab.imshow( (20*np.log10( 0.1 + freq2)).astype(int)), pylab.show()

Are you surprised? This is what the rhino image looks like, in its Fourier spectrum form: