# 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)

# 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)

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]