The following code block shows how to apply a Gaussian filter in the frequency domain using the convolution theorem and numpy fft (since in the frequency domain it is simply multiplication):
pylab.figure(figsize=(20,15))pylab.gray() # show the filtered result in grayscaleim = np.mean(imread('../images/lena.jpg'), axis=2)gauss_kernel = np.outer(signal.gaussian(im.shape[0], 5), signal.gaussian(im.shape[1], 5))freq = fp.fft2(im)assert(freq.shape == gauss_kernel.shape)freq_kernel = fp.fft2(fp.ifftshift(gauss_kernel))convolved = freq*freq_kernel # by the convolution theorem, simply multiply in the frequency domainim1 = fp.ifft2(convolved).realpylab.subplot(2,3,1), pylab.imshow(im), pylab.title('Original ...
