def ifft(z): B = z.shape[0]//2 L = z.shape[1] C = TT.as_tensor_variable(np.asarray([[[1,-1]]], dtype=T.config.floatX)) Zr, Zi = TTF.rfft(z[:B], norm="ortho"), TTF.rfft(z[B:]*-1, norm="ortho") isOdd = TT.eq(L%2, 1) Zr = TI.ifelse(isOdd, TT.concatenate([Zr, C*Zr[:,1: ][:,::-1]], axis=1), TT.concatenate([Zr, C*Zr[:,1:-1][:,::-1]], axis=1)) Zi = TI.ifelse(isOdd, TT.concatenate([Zi, C*Zi[:,1: ][:,::-1]], axis=1), TT.concatenate([Zi, C*Zi[:,1:-1][:,::-1]], axis=1)) Zi = (C*Zi)[:,:,::-1] # Zi * i Z = Zr+Zi return TT.concatenate([Z[:,:,0], Z[:,:,1]*-1], axis=0)
def test_params(self):
inputs_val = np.random.random((1, N)).astype(theano.config.floatX)
inputs = theano.shared(inputs_val)
with pytest.raises(ValueError):
fft.rfft(inputs, norm=123)
inputs_val = np.random.random((1, N // 2 + 1, 2)).astype(theano.config.floatX)
inputs = theano.shared(inputs_val)
with pytest.raises(ValueError):
fft.irfft(inputs, norm=123)
with pytest.raises(ValueError):
fft.irfft(inputs, is_odd=123)
def test_norm_rfft(self):
inputs_val = np.random.random((1, N, N)).astype(theano.config.floatX)
inputs = theano.shared(inputs_val)
# Unitary normalization
rfft = fft.rfft(inputs, norm="ortho")
f_rfft = theano.function([], rfft)
res_rfft = f_rfft()
res_rfft_comp = np.asarray(res_rfft[:, :, :, 0]) + 1j * np.asarray(
res_rfft[:, :, :, 1]
)
rfft_ref = np.fft.rfftn(inputs_val, axes=(1, 2))
utt.assert_allclose(rfft_ref / N, res_rfft_comp, atol=1e-4, rtol=1e-4)
# No normalization
rfft = fft.rfft(inputs, norm="no_norm")
f_rfft = theano.function([], rfft)
res_rfft = f_rfft()
res_rfft_comp = np.asarray(res_rfft[:, :, :, 0]) + 1j * np.asarray(
res_rfft[:, :, :, 1]
)
utt.assert_allclose(rfft_ref, res_rfft_comp, atol=1e-4, rtol=1e-4)
# Inverse FFT inputs
inputs_val = np.random.random((1, N, N // 2 + 1, 2)).astype(
theano.config.floatX
)
inputs = theano.shared(inputs_val)
inputs_ref = inputs_val[..., 0] + 1j * inputs_val[..., 1]
# Unitary normalization inverse FFT
irfft = fft.irfft(inputs, norm="ortho")
f_irfft = theano.function([], irfft)
res_irfft = f_irfft()
irfft_ref = np.fft.irfftn(inputs_ref, axes=(1, 2))
utt.assert_allclose(irfft_ref * N, res_irfft, atol=1e-4, rtol=1e-4)
# No normalization inverse FFT
irfft = fft.irfft(inputs, norm="no_norm")
f_irfft = theano.function([], irfft)
res_irfft = f_irfft()
utt.assert_allclose(irfft_ref * N ** 2, res_irfft, atol=1e-4, rtol=1e-4)
def test_irfft(self):
inputs_val = np.random.random((1, N, N)).astype(theano.config.floatX)
inputs = theano.shared(inputs_val)
rfft = fft.rfft(inputs)
f_rfft = theano.function([], rfft)
res_fft = f_rfft()
m = rfft.type()
irfft = fft.irfft(m)
f_irfft = theano.function([m], irfft)
res_irfft = f_irfft(res_fft)
utt.assert_allclose(inputs_val, np.asarray(res_irfft))
inputs_val = np.random.random(
(1, N, N, 2)).astype(theano.config.floatX)
inputs = theano.shared(inputs_val)
irfft = fft.irfft(inputs)
f_irfft = theano.function([], irfft)
res_irfft = f_irfft()
inputs_ref = inputs_val[..., 0] + inputs_val[..., 1] * 1j
irfft_ref = np.fft.irfftn(inputs_ref, axes=(1, 2))
utt.assert_allclose(irfft_ref, res_irfft, atol=1e-4, rtol=1e-4)
def Tfft2old(a): """ assumes len(a.shape)==2, does not assert this """ #A = np.zeros_like(a,dtype=np.complex_) s = a.shape[1] S = s//2+1 aa = T.stack([a],axis=0) AA = Tfft.rfft(aa) B = AA[...,0] + 1.j * AA[...,1] # Theano rfft stores complex values in separate array #return AA[0,...,0] #A[:,:S] = B # copy left half to right half #A[:,S:] = np.conj(np.fliplr(A[:,1:S-1])) #below no worky C = B[0,...] CC = C[:,1:S-1] return T.concatenate([C,T.conj(CC[:,::-1])],axis=1) A = T.zeros_like(a) #Alookup = theano.shared(A) Afront = A[:,:S] Aback = A[:,S:] A = T.set_subtensor(Afront,B) A = T.set_subtensor(Aback,T.conj(Tfftshift(A))[:,S:]) #A[:,:S] = B #A[:,S:] = T.conj(npfft.fftshift(A))[:,S:] return A
def test_1Drfft(self):
inputs_val = np.random.random((1, N)).astype(theano.config.floatX)
x = T.matrix('x')
rfft = fft.rfft(x)
f_rfft = theano.function([x], rfft)
res_rfft = f_rfft(inputs_val)
res_rfft_comp = (np.asarray(res_rfft[:, :, 0]) +
1j * np.asarray(res_rfft[:, :, 1]))
rfft_ref = np.fft.rfft(inputs_val, axis=1)
utt.assert_allclose(rfft_ref, res_rfft_comp)
m = rfft.type()
print(m.ndim)
irfft = fft.irfft(m)
f_irfft = theano.function([m], irfft)
res_irfft = f_irfft(res_rfft)
utt.assert_allclose(inputs_val, np.asarray(res_irfft))
# The numerical gradient of the FFT is sensitive, must set large
# enough epsilon to get good accuracy.
eps = 1e-1
def f_rfft(inp):
return fft.rfft(inp)
inputs_val = np.random.random((1, N)).astype(theano.config.floatX)
utt.verify_grad(f_rfft, [inputs_val], eps=eps)
def f_irfft(inp):
return fft.irfft(inp)
inputs_val = np.random.random((1, N // 2 + 1, 2)).astype(theano.config.floatX)
utt.verify_grad(f_irfft, [inputs_val], eps=eps)
def test_1Drfft(self):
inputs_val = numpy.random.random((1, N)).astype(theano.config.floatX)
x = T.matrix('x')
rfft = fft.rfft(x)
f_rfft = theano.function([x], rfft)
res_rfft = f_rfft(inputs_val)
res_rfft_comp = (numpy.asarray(res_rfft[:, :, 0]) +
1j * numpy.asarray(res_rfft[:, :, 1]))
rfft_ref = numpy.fft.rfft(inputs_val, axis=1)
utt.assert_allclose(rfft_ref, res_rfft_comp)
m = rfft.type()
print(m.ndim)
irfft = fft.irfft(m)
f_irfft = theano.function([m], irfft)
res_irfft = f_irfft(res_rfft)
utt.assert_allclose(inputs_val, numpy.asarray(res_irfft))
# The numerical gradient of the FFT is sensitive, must set large
# enough epsilon to get good accuracy.
eps = 1e-1
def f_rfft(inp):
return fft.rfft(inp)
inputs_val = numpy.random.random((1, N)).astype(theano.config.floatX)
utt.verify_grad(f_rfft, [inputs_val], eps=eps)
def f_irfft(inp):
return fft.irfft(inp)
inputs_val = numpy.random.random((1, N // 2 + 1, 2)).astype(theano.config.floatX)
utt.verify_grad(f_irfft, [inputs_val], eps=eps)
def test_irfft(self):
inputs_val = np.random.random((1, N, N)).astype(theano.config.floatX)
inputs = theano.shared(inputs_val)
rfft = fft.rfft(inputs)
f_rfft = theano.function([], rfft)
res_fft = f_rfft()
m = rfft.type()
irfft = fft.irfft(m)
f_irfft = theano.function([m], irfft)
res_irfft = f_irfft(res_fft)
utt.assert_allclose(inputs_val, np.asarray(res_irfft))
inputs_val = np.random.random((1, N, N, 2)).astype(theano.config.floatX)
inputs = theano.shared(inputs_val)
irfft = fft.irfft(inputs)
f_irfft = theano.function([], irfft)
res_irfft = f_irfft()
inputs_ref = inputs_val[..., 0] + inputs_val[..., 1] * 1j
irfft_ref = np.fft.irfftn(inputs_ref, axes=(1, 2))
utt.assert_allclose(irfft_ref, res_irfft, atol=1e-4, rtol=1e-4)
def theano_fft(x):
x_win = x
# zero-pad
frame = T.zeros((x.shape[0], NFFT))
frame = T.set_subtensor(frame[:, :x.shape[1]], x_win)
# apply FFT
x = fft.rfft(frame, norm='ortho')
# get first half of spectrum
x = x[:, :fbins]
# squared magnitude
x = x[:, :, 0]**2 + x[:, :, 1]**2
# floor (prevents log from going to -Inf)
x = T.maximum(x, 1e-9) # -90dB
# map to log domain where 0dB -> 1 and -90dB -> -1
x = (20.0 / 90.0) * T.log10(x) + 1.0
# scale to weigh errors
x = 0.1 * x
return x
def test_norm_rfft(self):
inputs_val = np.random.random((1, N, N)).astype(theano.config.floatX)
inputs = theano.shared(inputs_val)
# Unitary normalization
rfft = fft.rfft(inputs, norm='ortho')
f_rfft = theano.function([], rfft)
res_rfft = f_rfft()
res_rfft_comp = (np.asarray(res_rfft[:, :, :, 0]) +
1j * np.asarray(res_rfft[:, :, :, 1]))
rfft_ref = np.fft.rfftn(inputs_val, axes=(1, 2))
utt.assert_allclose(rfft_ref / N, res_rfft_comp, atol=1e-4, rtol=1e-4)
# No normalization
rfft = fft.rfft(inputs, norm='no_norm')
f_rfft = theano.function([], rfft)
res_rfft = f_rfft()
res_rfft_comp = (np.asarray(res_rfft[:, :, :, 0]) +
1j * np.asarray(res_rfft[:, :, :, 1]))
utt.assert_allclose(rfft_ref, res_rfft_comp, atol=1e-4, rtol=1e-4)
# Inverse FFT inputs
inputs_val = np.random.random((1, N, N // 2 + 1, 2)).astype(theano.config.floatX)
inputs = theano.shared(inputs_val)
inputs_ref = inputs_val[..., 0] + 1j * inputs_val[..., 1]
# Unitary normalization inverse FFT
irfft = fft.irfft(inputs, norm='ortho')
f_irfft = theano.function([], irfft)
res_irfft = f_irfft()
irfft_ref = np.fft.irfftn(inputs_ref, axes=(1, 2))
utt.assert_allclose(irfft_ref * N, res_irfft, atol=1e-4, rtol=1e-4)
# No normalization inverse FFT
irfft = fft.irfft(inputs, norm='no_norm')
f_irfft = theano.function([], irfft)
res_irfft = f_irfft()
utt.assert_allclose(irfft_ref * N**2, res_irfft, atol=1e-4, rtol=1e-4)
def y_fd(Tobs, f0, fdot, fddot, phi0, nhat, cos_iota, psi, heterodyne_bin, N):
fhet = heterodyne_bin / Tobs
ts = linspace(0, Tobs, N + 1)[:-1]
ys_re, ys_im = y_slow(ts,
f0,
fdot,
fddot,
phi0,
nhat,
cos_iota,
psi,
fhet=fhet)
ys_re_rfft = ttf.rfft(tt.reshape(ys_re, (-1, N)))
ys_im_rfft = ttf.rfft(tt.reshape(ys_im, (-1, N)))
NN = N // 2 + 1
ys_re_rfft = tt.reshape(ys_re_rfft, (3, 3, NN, 2))
ys_im_rfft = tt.reshape(ys_im_rfft, (3, 3, NN, 2))
y_fd_re = tt.zeros((3, 3, N))
y_fd_im = tt.zeros((3, 3, N))
y_fd_re = tt.set_subtensor(y_fd_re[:, :, :NN],
ys_re_rfft[:, :, :, 0] - ys_im_rfft[:, :, :, 1])
y_fd_im = tt.set_subtensor(y_fd_im[:, :, :NN],
ys_re_rfft[:, :, :, 1] + ys_im_rfft[:, :, :, 0])
y_fd_re = tt.set_subtensor(
y_fd_re[:, :, NN:],
ys_re_rfft[:, :, -2:0:-1, 0] + ys_im_rfft[:, :, -2:0:-1, 1])
y_fd_im = tt.set_subtensor(
y_fd_im[:, :, NN:],
-ys_re_rfft[:, :, -2:0:-1, 1] + ys_im_rfft[:, :, -2:0:-1, 0])
return 0.5 * (ts[1] - ts[0]) * y_fd_re, 0.5 * (ts[1] - ts[0]) * y_fd_im
def test_rfft(self):
inputs_val = np.random.random((1, N, N)).astype(theano.config.floatX)
inputs = theano.shared(inputs_val)
rfft = fft.rfft(inputs)
f_rfft = theano.function([], rfft)
res_rfft = f_rfft()
res_rfft_comp = (np.asarray(res_rfft[:, :, :, 0]) +
1j * np.asarray(res_rfft[:, :, :, 1]))
rfft_ref = np.fft.rfftn(inputs_val, axes=(1, 2))
utt.assert_allclose(rfft_ref, res_rfft_comp, atol=1e-4, rtol=1e-4)
def test_rfft(self):
inputs_val = np.random.random((1, N, N)).astype(theano.config.floatX)
inputs = theano.shared(inputs_val)
rfft = fft.rfft(inputs)
f_rfft = theano.function([], rfft)
res_rfft = f_rfft()
res_rfft_comp = (np.asarray(res_rfft[:, :, :, 0]) +
1j * np.asarray(res_rfft[:, :, :, 1]))
rfft_ref = np.fft.rfftn(inputs_val, axes=(1, 2))
utt.assert_allclose(rfft_ref, res_rfft_comp, atol=1e-4, rtol=1e-4)
def Tfft2(a): """ assumes len(a.shape)==2, does not assert this """ #A = np.zeros_like(a,dtype=np.complex_) s = a.shape[0] S = s//2+1 #aa = T.stack([a],axis=0) aa = a.reshape((1,a.shape[0],a.shape[1])) AA = Tfft.rfft(aa) B = AA[...,0] + 1.j * AA[...,1] # Theano rfft stores complex values in separate array # get first output C = B[0,...] CC = C[:,1:S-1] A = T.zeros_like(a) Afront = A[:,:S] A = T.set_subtensor(Afront,C) Aback = A[:,S:] A = T.set_subtensor(Aback,T.conj(Tfftshift(A))[:,S:]) return A
def call(self, x, mask=None):
for fr_idx in range(self.n_frame):
X_frame_power = K.sum(K.square(
fft.rfft(self.fft_window *
x[:, :, fr_idx * self.n_hop:fr_idx * self.n_hop +
self.n_fft])),
axis=3,
keepdims=True)
if fr_idx == 0:
output = X_frame_power
else:
output = T.concatenate([output, X_frame_power], axis=3)
if self.power_stft != 2.0:
output = K.pow(output, self.power_stft / 2.0)
if self.return_decibel_stft:
output = backend_keras.amplitude_to_decibel(output)
return output
def theano_fft(x):
# window with analysis window
x_win = win * x
# zero-pad
frame = T.zeros((x.shape[0], NFFT))
frame = T.set_subtensor(frame[:, :x.shape[1]], x_win)
# apply FFT
x = fft.rfft(frame, norm='ortho')
# get first half of spectrum
x = x[:, :fbins]
# squared magnitude
x = x[:, :, 0]**2 + x[:, :, 1]**2
# floor (prevents log from going to -Inf)
x = T.maximum(x, 1e-9)
return x
def f_rfft(inp):
return fft.rfft(inp)
def f_rfft(inp):
return fft.rfft(inp, norm='ortho')
def fft(x, norm=None):
'''Fast fourier transform:
Compute an n-point fft of frames along given axis.
'''
return rfft(x, norm=norm)
def f_rfft(inp):
return fft.rfft(inp)
def f_rfft(inp):
return fft.rfft(inp, norm='ortho')
def fft(x, norm=None):
'''Fast fourier transform:
Compute an n-point fft of frames along given axis.
'''
return rfft(x, norm=norm)
import numpy as np
import theano
import theano.tensor as T
from theano.tensor import fft
import theano.sandbox.fourier as tsf
import Image, ImageFilter
import matplotlib.pyplot as plt
im = Image.open('./pic/f.png')
x = T.matrix('x', dtype='float64')
rfft = fft.rfft(x)
y=rfft.type()
ifft = fft.irfft(y)
f_rfft = theano.function([x],rfft)
f_ifft = theano.function([y],ifft)
out = f_rfft(im)
rec=f_ifft(out)
plt.imshow(out[:,:,0], 'gray')
plt.imshow(rec, 'gray')
plt.show()
#c_out = np.asarray(out[0, :, 0] + 1j*out[0, :, 1])
#abs_out = abs(c_out)
def f_rfft(inp):
return fft.rfft(inp, norm="ortho")
