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dct.py
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dct.py
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import numpy as np
import torch
def dct1(x):
"""
Discrete Cosine Transform, Type I
:param x: the input signal
:return: the DCT-I of the signal over the last dimension
"""
x_shape = x.shape
x = x.view(-1, x_shape[-1])
return torch.fft.fft(torch.cat([x, x.flip([1])[:, 1:-1]], dim=1), 1).real.view(*x_shape)
def idct1(X):
"""
The inverse of DCT-I, which is just a scaled DCT-I
Our definition if idct1 is such that idct1(dct1(x)) == x
:param X: the input signal
:return: the inverse DCT-I of the signal over the last dimension
"""
n = X.shape[-1]
return dct1(X) / (2 * (n - 1))
def dct(x, norm=None):
"""
Discrete Cosine Transform, Type II (a.k.a. the DCT)
For the meaning of the parameter `norm`, see:
https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html
:param x: the input signal
:param norm: the normalization, None or 'ortho'
:return: the DCT-II of the signal over the last dimension
"""
x_shape = x.shape
N = x_shape[-1]
x = x.contiguous().view(-1, N)
v = torch.cat([x[:, ::2], x[:, 1::2].flip([1])], dim=1)
Vc = torch.fft.fft(v)
k = - torch.arange(N, dtype=x.dtype, device=x.device)[None, :] * np.pi / (2 * N)
W_r = torch.cos(k)
W_i = torch.sin(k)
# V = Vc[:, :, 0] * W_r - Vc[:, :, 1] * W_i
V = Vc.real * W_r - Vc.imag * W_i
if norm == 'ortho':
V[:, 0] /= np.sqrt(N) * 2
V[:, 1:] /= np.sqrt(N / 2) * 2
V = 2 * V.view(*x_shape)
return V
def idct(X, norm=None):
"""
The inverse to DCT-II, which is a scaled Discrete Cosine Transform, Type III
Our definition of idct is that idct(dct(x)) == x
For the meaning of the parameter `norm`, see:
https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html
:param X: the input signal
:param norm: the normalization, None or 'ortho'
:return: the inverse DCT-II of the signal over the last dimension
"""
x_shape = X.shape
N = x_shape[-1]
X_v = X.contiguous().view(-1, x_shape[-1]) / 2
if norm == 'ortho':
X_v[:, 0] *= np.sqrt(N) * 2
X_v[:, 1:] *= np.sqrt(N / 2) * 2
k = torch.arange(x_shape[-1], dtype=X.dtype, device=X.device)[None, :] * np.pi / (2 * N)
W_r = torch.cos(k)
W_i = torch.sin(k)
V_t_r = X_v
V_t_i = torch.cat([X_v[:, :1] * 0, -X_v.flip([1])[:, :-1]], dim=1)
V_r = V_t_r * W_r - V_t_i * W_i
V_i = V_t_r * W_i + V_t_i * W_r
V = torch.cat([V_r.unsqueeze(2), V_i.unsqueeze(2)], dim=2)
tmp = torch.complex(real=V[:, :, 0], imag=V[:, :, 1])
v = torch.fft.ifft(tmp)
x = v.new_zeros(v.shape)
x[:, ::2] += v[:, :N - (N // 2)]
x[:, 1::2] += v.flip([1])[:, :N // 2]
return x.view(*x_shape).real
def dct_2d(x, norm=None):
"""
2-dimentional Discrete Cosine Transform, Type II (a.k.a. the DCT)
For the meaning of the parameter `norm`, see:
https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html
:param x: the input signal
:param norm: the normalization, None or 'ortho'
:return: the DCT-II of the signal over the last 2 dimensions
"""
X1 = dct(x, norm=norm)
X2 = dct(X1.transpose(-1, -2), norm=norm)
return X2.transpose(-1, -2)
def idct_2d(X, norm=None):
"""
The inverse to 2D DCT-II, which is a scaled Discrete Cosine Transform, Type III
Our definition of idct is that idct_2d(dct_2d(x)) == x
For the meaning of the parameter `norm`, see:
https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html
:param X: the input signal
:param norm: the normalization, None or 'ortho'
:return: the DCT-II of the signal over the last 2 dimensions
"""
x1 = idct(X, norm=norm)
x2 = idct(x1.transpose(-1, -2), norm=norm)
return x2.transpose(-1, -2)
def dct_3d(x, norm=None):
"""
3-dimentional Discrete Cosine Transform, Type II (a.k.a. the DCT)
For the meaning of the parameter `norm`, see:
https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html
:param x: the input signal
:param norm: the normalization, None or 'ortho'
:return: the DCT-II of the signal over the last 3 dimensions
"""
X1 = dct(x, norm=norm)
X2 = dct(X1.transpose(-1, -2), norm=norm)
X3 = dct(X2.transpose(-1, -3), norm=norm)
return X3.transpose(-1, -3).transpose(-1, -2)
def idct_3d(X, norm=None):
"""
The inverse to 3D DCT-II, which is a scaled Discrete Cosine Transform, Type III
Our definition of idct is that idct_3d(dct_3d(x)) == x
For the meaning of the parameter `norm`, see:
https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html
:param X: the input signal
:param norm: the normalization, None or 'ortho'
:return: the DCT-II of the signal over the last 3 dimensions
"""
x1 = idct(X, norm=norm)
x2 = idct(x1.transpose(-1, -2), norm=norm)
x3 = idct(x2.transpose(-1, -3), norm=norm)
return x3.transpose(-1, -3).transpose(-1, -2)