text: import cv2
  import numpy as np
  import matplotlib.pyplot as plt
  
  
  # DFT hyper-parameters
  K, L = 128, 128
  channel = 3
  
  # bgr -> gray
  def bgr2gray(img):
  	gray = 0.2126 * img[..., 2] + 0.7152 * img[..., 1] + 0.0722 * img[..., 0]
  	return gray
  
  
  # DFT
  def dft(img):
  	# Prepare DFT coefficient
  	G = np.zeros((L, K, channel), dtype=np.complex)
  
  	# prepare processed index corresponding to original image positions
  	x = np.tile(np.arange(W), (H, 1))
  	y = np.arange(H).repeat(W).reshape(H, -1)
  
  	# dft
  	for c in range(channel):
  		for l in range(L):
  			for k in range(K):
  				G[l, k, c] = np.sum(img[..., c] * np.exp(-2j * np.pi * (x * k / K + y * l / L))) / np.sqrt(K * L)
  				#for n in range(N):
  				#    for m in range(M):
  				#        v += gray[n, m] * np.exp(-2j * np.pi * (m * k / M + n * l / N))
  				#G[l, k] = v / np.sqrt(M * N)
  
  	return G
  
  # IDFT
  def idft(G):
  	# prepare out image
  	H, W, _ = G.shape
  	out = np.zeros((H, W, channel), dtype=np.float32)
  
  	# prepare processed index corresponding to original image positions
  	x = np.tile(np.arange(W), (H, 1))
  	y = np.arange(H).repeat(W).reshape(H, -1)
  
  	# idft
  	for c in range(channel):
  		for l in range(H):
  			for k in range(W):
  				out[l, k, c] = np.abs(np.sum(G[..., c] * np.exp(2j * np.pi * (x * k / W + y * l / H)))) / np.sqrt(W * H)
  
  	# clipping
  	out = np.clip(out, 0, 255)
  	out = out.astype(np.uint8)
  
  	return out
  
  
  # HPF
  def hpf(G, ratio=0.1):
  	H, W, _ = G.shape	
  
  	# transfer positions
  	_G = np.zeros_like(G)
  	_G[:H//2, :W//2] = G[H//2:, W//2:]
  	_G[:H//2, W//2:] = G[H//2:, :W//2]
  	_G[H//2:, :W//2] = G[:H//2, W//2:]
  	_G[H//2:, W//2:] = G[:H//2, :W//2]
  
  	# get distance from center (H / 2, W / 2)
  	x = np.tile(np.arange(W), (H, 1))
  	y = np.arange(H).repeat(W).reshape(H, -1)
  
  	# make filter
  	_x = x - W // 2
  	_y = y - H // 2
  	r = np.sqrt(_x ** 2 + _y ** 2)
  	mask = np.ones((H, W), dtype=np.float32)
  	mask[r < (W // 2 * ratio)] = 0
  
  	mask = np.repeat(mask, channel).reshape(H, W, channel)
  
  	# filtering
  	_G *= mask
  
  	# reverse original positions
  	G[:H//2, :W//2] = _G[H//2:, W//2:]
  	G[:H//2, W//2:] = _G[H//2:, :W//2]
  	G[H//2:, :W//2] = _G[:H//2, W//2:]
  	G[H//2:, W//2:] = _G[:H//2, :W//2]
  
  	return G
  
  
  # Read image
  img = cv2.imread("imori.jpg").astype(np.float32)
  H, W, C = img.shape
  
  # Gray scale
  gray = bgr2gray(img)
  
  # DFT
  G = dft(img)
  
  # HPF
  G = hpf(G)
  
  # IDFT
  out = idft(G)
  
  # Save result
  cv2.imshow("result", out)
  cv2.waitKey(0)
  cv2.imwrite("out.jpg", out)
  