def gabor(signal, n_coeff=None, q_oversample=None, window=None):
"""Compute the Gabor representation of a signal.
:param signal: Singal to be analyzed.
:param n_coeff: number of Gabor coefficients in time.
:param q_oversample: Degree of oversampling
:param window: Synthesis window
:type signal: array-like
:type n_coeff: integer
:type q_oversample: int
:type window: array-like
:return: Tuple of Gabor coefficients, biorthogonal window associated with the synthesis window.
:rtype: tuple
"""
if n_coeff is None:
n_coeff = divider(signal.shape[0])
if q_oversample is None:
q_oversample = divider(n_coeff)
if window is None:
window = np.exp(np.log(0.005) * np.linspace(-1, 1, nearest_odd(n_coeff)) ** 2)
window = window / np.linalg.norm(window)
m = int(q_oversample * signal.shape[0] / float(n_coeff))
mb = int(signal.shape[0] / float(n_coeff))
nb = int(signal.shape[0] / float(m))
# Zak transform?
nh = window.shape[0]
if nh % 2 == 0:
raise ValueError("The window function should have an odd length.")
alpha = np.round((2 * signal.shape[0] / float(n_coeff) - 1 - nh) / (2 *
q_oversample))
hn1 = np.zeros((signal.shape[0],))
start = np.round(((signal.shape[0] - (nh - 1))) / 2) - alpha
end = np.round((signal.shape[0] + nh - 1) / 2) - alpha
hn1[np.arange(start - 1, end).astype(int)] = window
msig = hn1.reshape(int(nb), int(m), order='F')
dzth = np.fft.fft(msig.T, axis=0) / np.sqrt(m)
mzh = np.zeros((m, mb))
x = np.arange(1, m + 1, dtype=float)
for l in range(q_oversample):
mod = modulo(x - l * m / q_oversample, m).astype(int)
mzh += np.abs(dzth[mod - 1, :]) ** 2
mzh[mzh < np.spacing(1)] = 1
# Za transform of biorthogonal dual frame window gam
dztgam = dzth / mzh
gam = np.real(izak(dztgam)) / signal.shape[0]
# Computation of Gabor coefficient of dual frame window.
dgrn1 = np.zeros((signal.shape[0], n_coeff), dtype=complex)
k = np.arange(1, signal.shape[0] + 1)
for n in range(n_coeff):
index = modulo(k - n * m / q_oversample, signal.shape[0]).astype(int) - 1
dgrn1[:, n] = np.fft.fft(signal * np.fft.fftshift(gam[index]), axis=0)
dgr = dgrn1[np.arange(signal.shape[0], step=nb).astype(int), :]
tfr = np.abs(dgr) ** 2
return tfr, dgr, gam
def gabor(signal, n_coeff=None, q_oversample=None, window=None):
"""Compute the Gabor representation of a signal.
:param signal: Singal to be analyzed.
:param n_coeff: number of Gabor coefficients in time.
:param q_oversample: Degree of oversampling
:param window: Synthesis window
:type signal: array-like
:type n_coeff: integer
:type q_oversample: int
:type window: array-like
:return: Tuple of Gabor coefficients, biorthogonal window associated with the synthesis window.
:rtype: tuple
"""
if n_coeff is None:
n_coeff = divider(signal.shape[0])
if q_oversample is None:
q_oversample = divider(n_coeff)
if window is None:
window = np.exp(np.log(0.005) * np.linspace(-1, 1, nearest_odd(n_coeff)) ** 2)
window = window / np.linalg.norm(window)
m = int(q_oversample * signal.shape[0] / float(n_coeff))
mb = int(signal.shape[0] / float(n_coeff))
nb = int(signal.shape[0] / float(m))
# Zak transform?
nh = window.shape[0]
if nh % 2 == 0:
raise ValueError("The window function should have an odd length.")
alpha = np.round((2 * signal.shape[0] / float(n_coeff) - 1 - nh) / (2 *
q_oversample))
hn1 = np.zeros((signal.shape[0],))
start = np.round(((signal.shape[0] - (nh - 1))) / 2) - alpha
end = np.round((signal.shape[0] + nh - 1) / 2) - alpha
hn1[np.arange(start - 1, end).astype(int)] = window
msig = hn1.reshape(int(nb), int(m), order='F')
dzth = np.fft.fft(msig.T, axis=0) / np.sqrt(m)
mzh = np.zeros((m, mb))
x = np.arange(1, m + 1, dtype=float)
for l in range(q_oversample):
mod = modulo(x - l * m / q_oversample, m).astype(int)
mzh += np.abs(dzth[mod - 1, :]) ** 2
mzh[mzh < np.spacing(1)] = 1
# Za transform of biorthogonal dual frame window gam
dztgam = dzth / mzh
gam = np.real(izak(dztgam)) / signal.shape[0]
# Computation of Gabor coefficient of dual frame window.
dgrn1 = np.zeros((signal.shape[0], n_coeff), dtype=complex)
k = np.arange(1, signal.shape[0] + 1)
for n in range(n_coeff):
index = modulo(k - n * m / q_oversample, signal.shape[0]).astype(int) - 1
dgrn1[:, n] = np.fft.fft(signal * np.fft.fftshift(gam[index]), axis=0)
dgr = dgrn1[np.arange(signal.shape[0], step=nb).astype(int), :]
tfr = np.abs(dgr) ** 2
return tfr, dgr, gam
def test_modulo(self):
"""Test the modulo function."""
x = np.arange(1, 11)
np.testing.assert_allclose(utils.modulo(x, 1), np.ones(x.shape))
np.testing.assert_allclose(utils.modulo(x, 2),
np.array([1, 2, 1, 2, 1, 2, 1, 2, 1, 2]))
np.testing.assert_allclose(utils.modulo(x, 3),
np.array([1, 2, 3, 1, 2, 3, 1, 2, 3, 1]))
np.testing.assert_allclose(utils.modulo(x, 4),
np.array([1, 2, 3, 4, 1, 2, 3, 4, 1, 2]))
np.testing.assert_allclose(utils.modulo(x, 5),
np.array([1, 2, 3, 4, 5, 1, 2, 3, 4, 5]))
def test_modulo(self):
"""Test the modulo function."""
x = np.arange(1, 11)
np.testing.assert_allclose(utils.modulo(x, 1), np.ones(x.shape))
np.testing.assert_allclose(utils.modulo(x, 2),
np.array([1, 2, 1, 2, 1, 2, 1, 2, 1, 2]))
np.testing.assert_allclose(utils.modulo(x, 3),
np.array([1, 2, 3, 1, 2, 3, 1, 2, 3, 1]))
np.testing.assert_allclose(utils.modulo(x, 4),
np.array([1, 2, 3, 4, 1, 2, 3, 4, 1, 2]))
np.testing.assert_allclose(utils.modulo(x, 5),
np.array([1, 2, 3, 4, 5, 1, 2, 3, 4, 5]))