def test_stft():
"Test stft and istft tight frame property"
sfreq = 1000. # Hz
f = 7. # Hz
for T in [253, 256]: # try with even and odd numbers
t = np.arange(T).astype(np.float)
x = np.sin(2 * np.pi * f * t / sfreq)
x = np.array([x, x + 1.])
wsize = 128
tstep = 4
X = stft(x, wsize, tstep)
xp = istft(X, tstep, Tx=T)
freqs = stftfreq(wsize, sfreq=1000)
max_freq = freqs[np.argmax(np.sum(np.abs(X[0])**2, axis=1))]
assert_true(X.shape[1] == len(freqs))
assert_true(np.all(freqs >= 0.))
assert_true(np.abs(max_freq - f) < 1.)
assert_array_almost_equal(x, xp, decimal=6)
# norm conservation thanks to tight frame property
assert_almost_equal(np.sqrt(stft_norm2(X)),
map(linalg.norm, x),
decimal=2)
# Try with empty array
x = np.zeros((0, T))
X = stft(x, wsize, tstep)
xp = istft(X, tstep, T)
assert_true(xp.shape == x.shape)
def test_stft():
"Test stft and istft tight frame property"
sfreq = 1000. # Hz
f = 7. # Hz
for T in [253, 256]: # try with even and odd numbers
t = np.arange(T).astype(np.float)
x = np.sin(2 * np.pi * f * t / sfreq)
x = np.array([x, x + 1.])
wsize = 128
tstep = 4
X = stft(x, wsize, tstep)
xp = istft(X, tstep, Tx=T)
freqs = stftfreq(wsize, sfreq=1000)
max_freq = freqs[np.argmax(np.sum(np.abs(X[0]) ** 2, axis=1))]
assert_true(X.shape[1] == len(freqs))
assert_true(np.all(freqs >= 0.))
assert_true(np.abs(max_freq - f) < 1.)
assert_array_almost_equal(x, xp, decimal=6)
# norm conservation thanks to tight frame property
assert_almost_equal(np.sqrt(stft_norm2(X)),
[linalg.norm(xx) for xx in x], decimal=2)
# Try with empty array
x = np.zeros((0, T))
X = stft(x, wsize, tstep)
xp = istft(X, tstep, T)
assert_true(xp.shape == x.shape)
def test_stft():
"""Test stft and istft tight frame property."""
sfreq = 1000. # Hz
f = 7. # Hz
for T in [127, 128]: # try with even and odd numbers
# Test with low frequency signal
t = np.arange(T).astype(np.float)
x = np.sin(2 * np.pi * f * t / sfreq)
x = np.array([x, x + 1.])
wsize = 128
tstep = 4
X = stft(x, wsize, tstep)
xp = istft(X, tstep, Tx=T)
freqs = stftfreq(wsize, sfreq=1000)
max_freq = freqs[np.argmax(np.sum(np.abs(X[0])**2, axis=1))]
assert X.shape[1] == len(freqs)
assert np.all(freqs >= 0.)
assert np.abs(max_freq - f) < 1.
assert_array_almost_equal(x, xp, decimal=6)
# norm conservation thanks to tight frame property
assert_almost_equal(np.sqrt(stft_norm2(X)),
[linalg.norm(xx) for xx in x],
decimal=6)
# Test with random signal
x = np.random.randn(2, T)
wsize = 16
tstep = 8
X = stft(x, wsize, tstep)
xp = istft(X, tstep, Tx=T)
freqs = stftfreq(wsize, sfreq=1000)
max_freq = freqs[np.argmax(np.sum(np.abs(X[0])**2, axis=1))]
assert X.shape[1] == len(freqs)
assert np.all(freqs >= 0.)
assert_array_almost_equal(x, xp, decimal=6)
# norm conservation thanks to tight frame property
assert_almost_equal(np.sqrt(stft_norm2(X)),
[linalg.norm(xx) for xx in x],
decimal=6)
# Try with empty array
x = np.zeros((0, T))
X = stft(x, wsize, tstep)
xp = istft(X, tstep, T)
assert xp.shape == x.shape
def fit(self, data):
""" Fit data
Parameters
---------
data : ndarray, shape (channels, times)
"""
print "First do stft"
stft_ = stft(data, self.wsize, self.tstep)
# bandpass filter
if self.sfreq:
freqs = stftfreq(self.wsize, self.sfreq)
hpass, lpass = 0, len(freqs)
if self.hpass:
hpass = min(np.where(freqs >= self.hpass)[0])
if self.lpass:
lpass = max(np.where(freqs <= self.lpass)[0])
self._freqs = freqs[hpass:lpass]
stft_ = stft_[:, hpass:lpass, :]
# store shape to retrieve it later
self._stft_shape = stft_.shape
# concatenate data
data2d = self._concat(stft_)
print "Whiten data"
dewhitening, whitened = self._whiten(data2d)
print "Do ICA"
mixing_, ic_ = self._fastica(whitened)
# sort according to objective value
objectives = []
for i in range(ic_.shape[0]):
component = ic_[i, :]
g_ = np.log(1 + np.abs(component)**2)
objectives.append(np.mean(g_))
indices = np.argsort(objectives)[::-1]
sorted_ic = ic_[np.argsort(objectives), :]
sorted_mixing = mixing_[:, np.argsort(objectives)]
# store for retrieving
self._mixing = sorted_mixing
self._dewhitening = dewhitening
self._source_stft = self._split(sorted_ic)
stc_data[0][:len(Ws[0])] = np.real(Ws[0]) stc_data[1][:len(Ws[1])] = np.real(Ws[1]) x = stc_data plt.plot(x.T) plt.show() n_times = x.shape[1] wsize = 16 tstep = 4 n_freq = wsize // 2 + 1 n_step = n_step = int(ceil(n_times / float(tstep))) sparse_phi = sparse_Phi(wsize, tstep) sparse_phiT = sparse_PhiT(tstep, n_freq, n_step, n_times) # =============== test stft==================================================== X0= stft(x, wsize = wsize, tstep = tstep ) X0_norm = np.abs(X0[0,:,:,]) active_t_ind = np.any(X0_norm>1E-3, axis=0) X1_sparse = sparse_stft(x,wsize, tstep, active_t_ind) X1 = np.zeros(X0.shape, dtype =np.complex) X1[:,:, active_t_ind] = X1_sparse X1_sparse_vec = sparse_phi(x,active_t_ind) X1_sparse_vec_mat = np.reshape(X1_sparse_vec,[2,n_freq,-1]) print np.linalg.norm(X1_sparse - X1_sparse_vec_mat) # order, 3d array, the outer part is the first, the innter part is the last # C order: # ‘C’ means to read / write the elements using C-like index order, # with the last axis index changing fastest, # back to the first axis index changing slowest.
