Exemple #1
0
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)
Exemple #2
0
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)