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 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
# 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_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=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_true(X.shape[1] == len(freqs))
assert_true(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_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)),
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_norm_epsilon():
"""Test computation of espilon norm on TF coefficients."""
n_steps = 5
n_freqs = 4
Y = np.zeros(n_steps * n_freqs)
l1_ratio = 0.5
assert_allclose(norm_epsilon(Y, l1_ratio, n_steps), 0.)
Y[0] = 2.
assert_allclose(norm_epsilon(Y, l1_ratio, n_steps), np.max(Y))
l1_ratio = 1.
assert_allclose(norm_epsilon(Y, l1_ratio, n_steps), np.max(Y))
# dummy value without random:
Y = np.arange(n_steps * n_freqs).reshape(-1, )
l1_ratio = 0.
assert_allclose(
norm_epsilon(Y, l1_ratio, n_steps)**2,
stft_norm2(Y.reshape(-1, n_freqs, n_steps)))
def test_norm_epsilon():
"""Test computation of espilon norm on TF coefficients."""
tstep = np.array([2])
wsize = np.array([4])
n_times = 10
n_steps = np.ceil(n_times / tstep.astype(float)).astype(int)
n_freqs = wsize // 2 + 1
n_coefs = n_steps * n_freqs
phi = _Phi(wsize, tstep, n_coefs)
Y = np.zeros(n_steps * n_freqs)
l1_ratio = 0.5
assert_allclose(norm_epsilon(Y, l1_ratio, phi), 0.)
Y[0] = 2.
assert_allclose(norm_epsilon(Y, l1_ratio, phi), np.max(Y))
l1_ratio = 1.
assert_allclose(norm_epsilon(Y, l1_ratio, phi), np.max(Y))
# dummy value without random:
Y = np.arange(n_steps * n_freqs).reshape(-1, )
l1_ratio = 0.
assert_allclose(norm_epsilon(Y, l1_ratio, phi) ** 2,
stft_norm2(Y.reshape(-1, n_freqs[0], n_steps[0])))
def test_norm_epsilon():
"""Test computation of espilon norm on TF coefficients."""
tstep = np.array([2])
wsize = np.array([4])
n_times = 10
n_steps = np.ceil(n_times / tstep.astype(float)).astype(int)
n_freqs = wsize // 2 + 1
n_coefs = n_steps * n_freqs
phi = _Phi(wsize, tstep, n_coefs)
Y = np.zeros(n_steps * n_freqs)
l1_ratio = 0.5
assert_allclose(norm_epsilon(Y, l1_ratio, phi), 0.)
Y[0] = 2.
assert_allclose(norm_epsilon(Y, l1_ratio, phi), np.max(Y))
l1_ratio = 1.
assert_allclose(norm_epsilon(Y, l1_ratio, phi), np.max(Y))
# dummy value without random:
Y = np.arange(n_steps * n_freqs).reshape(-1, )
l1_ratio = 0.
assert_allclose(
norm_epsilon(Y, l1_ratio, phi)**2,
stft_norm2(Y.reshape(-1, n_freqs[0], n_steps[0])))