def circular_correlation(self, left_x, right_x):
"""
Computes the circular correlation of two vectors a and b via their fast fourier transforms
In python code, ifft(np.conj(fft(a)) * fft(b)).real
:param left_x: ()
:param right_x:
(a - j * b) * (c + j * d) = (ac + bd) + j * (ad - bc)
:return:
"""
left_x_real = left_x
left_x_imag = chainer.as_variable(
self.xp.zeros_like(left_x_real, dtype=self.xp.float32))
left_x_fft_real, left_x_fft_imag = functions.fft(
(left_x_real, left_x_imag))
right_x_real = right_x
right_x_imag = chainer.as_variable(
self.xp.zeros_like(right_x_real, dtype=self.xp.float32))
right_x_fft_real, right_x_fft_imag = functions.fft(
(right_x_real, right_x_imag))
prod_fft_real = left_x_fft_real * right_x_fft_real + left_x_fft_imag * right_x_fft_imag
prod_fft_imag = left_x_fft_real * right_x_fft_imag - left_x_fft_imag * right_x_fft_real
ifft_real, _ = functions.ifft((prod_fft_real, prod_fft_imag))
return ifft_real
def fourier_transform(self, x):
"""
:param x: (mb, N, hidden_dim)
:return: tuple of x_fft_real and x_fft_imag, (mb, N, hidden_dim)
"""
x_real = x
x_imag = chainer.as_variable(
self.xp.zeros_like(x_real, dtype=self.xp.float32))
x_fft_real, x_fft_imag = functions.fft((x_real, x_imag))
return x_fft_real, x_fft_imag
def chainer_fft_spectrogram(xr, xi, forward=True):
T, O = xr.shape
if (forward): # STFT
yr, yi = F.fft((xr, xi))
yr = F.transpose(yr[:, :int(O / 2) + 1])
yi = F.transpose(yi[:, :int(O / 2) + 1])
else: # iSTFT
xr_cnj = F.fliplr(xr[:, 1:O - 1])
xi_cnj = -F.fliplr(xi[:, 1:O - 1])
xr = F.concat((xr, xr_cnj), axis=1)
xi = F.concat((xi, xi_cnj), axis=1)
yr, yi = F.ifft((xr, xi))
yr = F.transpose(yr)
yi = F.transpose(yi)
return yr, yi
def stft(x, frame_length=1024, hop_length=512):
# ..., FFT axis
if not isinstance(x, chainer.Variable):
x = chainer.as_variable(x)
xp = x.xp
pad_len = (x.shape[-1] // hop_length - frame_length // hop_length +
1) * hop_length + frame_length
pad = pad_len - x.shape[-1]
if pad > 0:
shape = list(x.shape)
pad = xp.zeros(shape[:-1] + [pad]).astype(x.dtype)
x = F.concat((x, pad), -1)
index = frame(np.arange(x.shape[-1]), frame_length, hop_length).T
tmp = x[..., index] * xp.hamming(frame_length).astype(x.dtype)
yr, yi = F.fft((tmp, xp.zeros(tmp.shape).astype(x.dtype)))
return yr[..., :frame_length // 2 + 1], yi[..., :frame_length // 2 + 1]
def stft(x, window):
# print(x.dtype)
wSize = window.shape[0]
xSize = x.shape[-1]
bSize = x.shape[0]
x = x.reshape(bSize, 1, xSize)
# h = xp.vstack([x[i:xSize-wSize+i] for i in range(256)]).T
# h = F.transpose(F.vstack([x[:,i:xSize-wSize+i] for i in range(wSize)]), axes=(0,2,1))
h = F.concat([x[:, :, i:xSize - wSize + i + 1] for i in range(wSize)],
axis=1)
h = F.transpose(h, axes=(0, 2, 1))
h = h.reshape(bSize, 1, xSize - wSize + 1, wSize)
# print(h.dtype)
# print(h.dtype)
h = h * window
h = F.fft((h, xp.zeros(h.shape, dtype=xp.float32)))
h = F.concat((h[0], h[1]), axis=1)
h = F.transpose(h, axes=(0, 1, 3, 2))
return h