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%matplotlib inline

Fast Fourier Transform snippets

Documentation

Numpy implementation: http://docs.scipy.org/doc/numpy/reference/routines.fft.html
Scipy implementation: http://docs.scipy.org/doc/scipy/reference/fftpack.html

Import directives



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import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm

Make data



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pattern = np.zeros((4, 4))
pattern[1:3,1:3] = 1



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pattern



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signal = np.tile(pattern, (2, 2))



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fig = plt.figure(figsize=(16.0, 10.0))
ax = fig.add_subplot(111)
ax.imshow(signal, interpolation='nearest', cmap=cm.gray)

Fourier transform with Numpy

Do the fourier transform



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transformed_signal = np.fft.fft2(signal)
#transformed_signal



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fig = plt.figure(figsize=(16.0, 10.0))
ax = fig.add_subplot(111)
ax.imshow(abs(transformed_signal), interpolation='nearest', cmap=cm.gray)

Filter



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max_value = np.max(abs(transformed_signal))
filtered_transformed_signal = transformed_signal * (abs(transformed_signal) > max_value*0.5)



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#filtered_transformed_signal[6, 6] = 0
#filtered_transformed_signal[2, 2] = 0
#filtered_transformed_signal[2, 6] = 0
#filtered_transformed_signal[6, 2] = 0
#filtered_transformed_signal[1, 6] = 0
#filtered_transformed_signal[6, 1] = 0
#filtered_transformed_signal[1, 2] = 0
#filtered_transformed_signal[2, 1] = 0

#filtered_transformed_signal

fig = plt.figure(figsize=(16.0, 10.0))
ax = fig.add_subplot(111)
ax.imshow(abs(filtered_transformed_signal), interpolation='nearest', cmap=cm.gray)

Do the reverse transform



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filtered_signal = np.fft.ifft2(filtered_transformed_signal)
#filtered_signal



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fig = plt.figure(figsize=(16.0, 10.0))
ax = fig.add_subplot(111)
ax.imshow(abs(filtered_signal), interpolation='nearest', cmap=cm.gray)



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#shifted_filtered_signal = np.fft.ifftshift(transformed_signal)
#shifted_filtered_signal



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#shifted_transformed_signal = np.fft.fftshift(transformed_signal)
#shifted_transformed_signal