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
# test if phi is still linear, it does not seems neumerically linear?
A = np.random.randn(2,2)
X1_sparse_vec1 = sparse_phi(A.dot(x),active_t_ind)
X1_sparse_vec2 = A.dot(sparse_phi(x,active_t_ind))
print np.linalg.norm(X1_sparse_vec1-X1_sparse_vec2) \
/np.linalg.norm(X1_sparse_vec1)
#=========== Note, a potential caveate of the mne's sparse representation=====
# even if the stft coefs Z are sparse in time, after phiH and phi, it would be
# sparse, the non-active set will have very small values near zero.
# this may be why my algorithms are very slow,
# and the L2 version of it does not work well
# ================ test istft==================================================
x0 = istft(X0, tstep = tstep)
x1 = sparse_istft(X1_sparse,tstep, active_t_ind)
x1_phi = sparse_phiT(X1_sparse_vec,active_t_ind)
plt.figure()
plt.plot(x0.T,'r')
plt.plot(x1.T,'g')
plt.plot(x.T,'b')
plt.plot(x1_phi.T,'m')
plt.show()
x11 = sparse_phiT(A.dot(X1_sparse_vec), active_t_ind)
x12 = A.dot(sparse_phiT(X1_sparse_vec, active_t_ind))
print np.linalg.norm(x11-x12) \
/np.linalg.norm(x12)