import numpy as np

img = plt.imread("Q2.tif")
N,M = np.shape(img)
i, j = np.meshgrid(np.arange(M), np.arange(N))
mult_factor = np.power( np.ones((N,M)) * -1 , i + j )
tmp = img * mult_factor
print("Calculating DFT")
dft = np.fft.fft2(tmp)
print("Calculating inverse DFT")
idft = np.fft.ifft2(dft.conj())
out_img = np.abs((mult_factor * idft.real) + (1j * idft.imag))