def run(self):
f = np.logspace(np.log10(self.fmin), np.log10(self.fmax), self.n_voices)
a = np.logspace(np.log10(self.fmax / float(self.fmin)), np.log10(1), self.n_voices)
wt = np.zeros((self.n_voices, self.ts.shape[0]), dtype=complex)
if self.waveparams > 0:
for ptr in range(self.n_voices):
nha = self.waveparams * a[ptr]
tha = np.arange(-int(np.round(nha)), int(np.round(nha)) + 1)
x = np.exp(-(2 * np.log(10) / (nha ** 2)) * tha ** 2)
y = np.exp(1j * 2 * np.pi * f[ptr] * tha)
ha = x * y
detail = np.convolve(self.z, ha) / np.sqrt(a[ptr])
ix = np.arange(int(np.round(nha)), detail.shape[0] - int(np.round(nha)) + 1,
dtype=int)
wt[ptr, :] = detail[self.ts]
detail = detail[ix]
self.tfr[ptr, :] = detail[self.ts] * np.conj(detail[self.ts])
elif self.waveparams == 0:
for ptr in range(self.n_voices):
ha = mexhat(f[ptr])
nha = (ha.shape[0] - 1) / 2
detail = np.convolve(self.z, ha) / np.sqrt(a[ptr])
ix = np.arange(int(np.round(nha)) + 1, detail.shape[0] - int(np.round(nha)) + 1)
detail = detail[ix]
wt[ptr, :] = detail[self.ts]
self.tfr[ptr, :] = detail[self.ts] * np.conj(detail[self.ts])
elif isinstance(self.waveparams, np.ndarray):
rwav, cwav = self.waveparams.shape
if cwav > rwav:
self.waveparams = self.waveparams.T
wavef = np.fft.fft(self.waveparams, axis=0)
nwave = self.waveparams.shape[0]
f0 = wavef[np.abs(wavef[:nwave / 2]) == np.amax(np.abs(wavef[:nwave / 2]))]
f0 = ((f0 - 1) * (1 / nwave)).mean()
a = np.logspace(np.log10(f0 / float(self.fmin)), np.log10(f0 / float(self.fmax)), self.n_voices)
B = 0.99
R = B / (1.001 / 2)
nscale = np.max([128, np.round((B * nwave * (1 + 2.0 / R) * np.log((1 +
R / 2.0) / (1 - R / 2.0))) / 2)])
wts = scale(self.waveparams, a, self.fmin, self.fmax, nscale)
for ptr in range(self.n_voices):
ha = wts[ptr, :]
nha = ha.shape[0] / 2
detail = np.convolve(self.z, ha) / np.sqrt(a[ptr])
detail = detail[int(np.floor(nha)):(detail.shape[0] - np.round(nha))]
wt[ptr, :] = detail[self.ts]
self.tfr[ptr, :] = detail[self.ts] * np.conj(detail[self.ts])
# Normalization
SP = np.fft.fft(self.z, axis=0)
indmin = 1 + int(np.round(self.fmin * (self.signal.shape[0] - 2)))
indmax = 1 + int(np.round(self.fmax * (self.signal.shape[0] - 2)))
SPana = SP[indmin:(indmax + 1)]
self.tfr = np.real(self.tfr)
self.tfr = self.tfr * (np.linalg.norm(SPana) ** 2) / integrate_2d(self.tfr, self.ts, f) / self.n_voices
return self.tfr, self.ts, f, wt
def scalogram(signal,
fmin=None,
fmax=None,
n_voices=None,
time_instants=None,
waveparams=None):
"""scalogram
:param signal:
:param fmin:
:param fmax:
:param n_voices:
:param time_instants:
:param waveparams:
:type signal:
:type fmin:
:type fmax:
:type n_voices:
:type time_instants:
:type waveparams:
:return:
:rtype:
"""
# FIXME: Output from the MATLAB implementation differs significantly.
if time_instants is None:
time_instants = np.arange(signal.shape[0])
if waveparams is None:
waveparams = np.sqrt(signal.shape[0])
if n_voices is None:
n_voices = signal.shape[0]
s_centered = np.real(signal) - np.real(signal).mean()
z = hilbert(s_centered)
if (fmin is None) or (fmax is None):
stf = np.fft.fft(
np.fft.fftshift(z[time_instants.min():time_instants.max() + 1]))
nstf = stf.shape[0]
sp = np.abs(stf[:int(np.round(nstf / 2.0))])**2
maxsp = sp.max()
f = np.linspace(0, 0.5, np.round(nstf / 2.0) + 1)
if fmin is None:
mask = sp > maxsp / 100.0
indmin = np.arange(mask.shape[0],
dtype=int)[mask.astype(bool)].min()
fmin = max([0.01, 0.05 * np.floor(f[indmin] / 0.05)])
if fmax is None:
mask = sp > maxsp / 100.0
indmax = np.arange(mask.shape[0],
dtype=int)[mask.astype(bool)].max()
fmax = 0.05 * np.ceil(f[indmax] / 0.05)
f = np.logspace(np.log10(fmin), np.log10(fmax), n_voices)
a = np.logspace(np.log10(fmax / float(fmin)), np.log10(1), n_voices)
wt = np.zeros((n_voices, time_instants.shape[0]), dtype=complex)
tfr = np.zeros((n_voices, time_instants.shape[0]), dtype=complex)
if waveparams > 0:
for ptr in xrange(n_voices):
nha = waveparams * a[ptr]
tha = np.arange(-np.round(nha), np.round(nha) + 1)
x = np.exp(-(2 * np.log(10) / (nha**2)) * tha**2)
y = np.exp(1j * 2 * np.pi * f[ptr] * tha)
ha = x * y
detail = np.convolve(z, ha) / np.sqrt(a[ptr])
ix = np.arange(round(nha),
detail.shape[0] - np.round(nha) + 1,
dtype=int)
wt[ptr, :] = detail[time_instants]
detail = detail[ix]
tfr[ptr, :] = detail[time_instants] * np.conj(
detail[time_instants])
elif waveparams == 0:
for ptr in xrange(n_voices):
ha = mexhat(f[ptr])
nha = (ha.shape[0] - 1) / 2
detail = np.convolve(z, ha) / np.sqrt(a[ptr])
ix = np.arange(round(nha) + 1, detail.shape[0] - np.round(nha) + 1)
detail = detail[ix]
wt[ptr, :] = detail[time_instants]
tfr[ptr, :] = detail[time_instants] * np.conj(
detail[time_instants])
elif isinstance(waveparams, np.ndarray):
rwav, cwav = waveparams.shape
if cwav > rwav:
waveparams = waveparams.T
wavef = np.fft.fft(waveparams, axis=0)
nwave = waveparams.shape[0]
f0 = wavef[np.abs(wavef[:nwave /
2]) == np.amax(np.abs(wavef[:nwave / 2]))]
f0 = ((f0 - 1) * (1 / nwave)).mean()
a = np.logspace(np.log10(f0 / float(fmin)), np.log10(f0 / float(fmax)),
n_voices)
B = 0.99
R = B / (1.001 / 2)
nscale = np.max([
128,
np.round((B * nwave * (1 + 2.0 / R) * np.log(
(1 + R / 2.0) / (1 - R / 2.0))) / 2)
])
wts = scale(waveparams, a, fmin, fmax, nscale)
for ptr in xrange(n_voices):
ha = wts[ptr, :]
nha = ha.shape[0] / 2
detail = np.convolve(z, ha) / np.sqrt(a[ptr])
detail = detail[int(np.floor(nha)):(detail.shape[0] -
np.round(nha))]
wt[ptr, :] = detail[time_instants]
tfr[ptr, :] = detail[time_instants] * np.conj(
detail[time_instants])
t = time_instants
f = f.T
# Normalization
SP = np.fft.fft(z, axis=0)
indmin = 1 + np.round(fmin * (signal.shape[0] - 2))
indmax = 1 + np.round(fmax * (signal.shape[0] - 2))
SPana = SP[indmin:(indmax + 1)]
tfr = np.real(tfr)
tfr = tfr * (np.linalg.norm(SPana)**2) / integrate_2d(tfr, t, f) / n_voices
return tfr, t, f, wt
def scalogram(signal, fmin=None, fmax=None, n_voices=None, time_instants=None,
waveparams=None):
"""scalogram
:param signal:
:param fmin:
:param fmax:
:param n_voices:
:param time_instants:
:param waveparams:
:type signal:
:type fmin:
:type fmax:
:type n_voices:
:type time_instants:
:type waveparams:
:return:
:rtype:
"""
# FIXME: Output from the MATLAB implementation differs significantly.
if time_instants is None:
time_instants = np.arange(signal.shape[0])
if waveparams is None:
waveparams = np.sqrt(signal.shape[0])
if n_voices is None:
n_voices = signal.shape[0]
s_centered = np.real(signal) - np.real(signal).mean()
z = hilbert(s_centered)
if (fmin is None) or (fmax is None):
stf = np.fft.fft(np.fft.fftshift(z[time_instants.min():time_instants.max() + 1]))
nstf = stf.shape[0]
sp = np.abs(stf[:int(np.round(nstf / 2.0))]) ** 2
maxsp = sp.max()
f = np.linspace(0, 0.5, np.round(nstf / 2.0) + 1)
if fmin is None:
mask = sp > maxsp / 100.0
indmin = np.arange(mask.shape[0], dtype=int)[mask.astype(bool)].min()
fmin = max([0.01, 0.05 * np.floor(f[indmin] / 0.05)])
if fmax is None:
mask = sp > maxsp / 100.0
indmax = np.arange(mask.shape[0], dtype=int)[mask.astype(bool)].max()
fmax = 0.05 * np.ceil(f[indmax] / 0.05)
f = np.logspace(np.log10(fmin), np.log10(fmax), n_voices)
a = np.logspace(np.log10(fmax / float(fmin)), np.log10(1), n_voices)
wt = np.zeros((n_voices, time_instants.shape[0]), dtype=complex)
tfr = np.zeros((n_voices, time_instants.shape[0]), dtype=complex)
if waveparams > 0:
for ptr in range(n_voices):
nha = waveparams * a[ptr]
tha = np.arange(-np.round(nha), np.round(nha) + 1)
x = np.exp(-(2 * np.log(10) / (nha ** 2)) * tha ** 2)
y = np.exp(1j * 2 * np.pi * f[ptr] * tha)
ha = x * y
detail = np.convolve(z, ha) / np.sqrt(a[ptr])
ix = np.arange(round(nha), detail.shape[0] - np.round(nha) + 1,
dtype=int)
wt[ptr, :] = detail[time_instants]
detail = detail[ix]
tfr[ptr, :] = detail[time_instants] * np.conj(detail[time_instants])
elif waveparams == 0:
for ptr in range(n_voices):
ha = mexhat(f[ptr])
nha = (ha.shape[0] - 1) / 2
detail = np.convolve(z, ha) / np.sqrt(a[ptr])
ix = np.arange(round(nha) + 1, detail.shape[0] - np.round(nha) + 1)
detail = detail[ix]
wt[ptr, :] = detail[time_instants]
tfr[ptr, :] = detail[time_instants] * np.conj(detail[time_instants])
elif isinstance(waveparams, np.ndarray):
rwav, cwav = waveparams.shape
if cwav > rwav:
waveparams = waveparams.T
wavef = np.fft.fft(waveparams, axis=0)
nwave = waveparams.shape[0]
f0 = wavef[np.abs(wavef[:nwave / 2]) == np.amax(np.abs(wavef[:nwave / 2]))]
f0 = ((f0 - 1) * (1 / nwave)).mean()
a = np.logspace(np.log10(f0 / float(fmin)), np.log10(f0 / float(fmax)), n_voices)
B = 0.99
R = B / (1.001 / 2)
nscale = np.max([128, np.round((B * nwave * (1 + 2.0 / R) * np.log((1 +
R / 2.0) / (1 - R / 2.0))) / 2)])
wts = scale(waveparams, a, fmin, fmax, nscale)
for ptr in range(n_voices):
ha = wts[ptr, :]
nha = ha.shape[0] / 2
detail = np.convolve(z, ha) / np.sqrt(a[ptr])
detail = detail[int(np.floor(nha)):(detail.shape[0] - np.round(nha))]
wt[ptr, :] = detail[time_instants]
tfr[ptr, :] = detail[time_instants] * np.conj(detail[time_instants])
t = time_instants
f = f.T
# Normalization
SP = np.fft.fft(z, axis=0)
indmin = 1 + np.round(fmin * (signal.shape[0] - 2))
indmax = 1 + np.round(fmax * (signal.shape[0] - 2))
SPana = SP[indmin:(indmax + 1)]
tfr = np.real(tfr)
tfr = tfr * (np.linalg.norm(SPana) ** 2) / integrate_2d(tfr, t, f) / n_voices
return tfr, t, f, wt
def run(self):
f = np.logspace(np.log10(self.fmin), np.log10(self.fmax),
self.n_voices)
a = np.logspace(np.log10(self.fmax / float(self.fmin)), np.log10(1),
self.n_voices)
wt = np.zeros((self.n_voices, self.ts.shape[0]), dtype=complex)
if self.waveparams > 0:
for ptr in range(self.n_voices):
nha = self.waveparams * a[ptr]
tha = np.arange(-int(np.round(nha)), int(np.round(nha)) + 1)
x = np.exp(-(2 * np.log(10) / (nha**2)) * tha**2)
y = np.exp(1j * 2 * np.pi * f[ptr] * tha)
ha = x * y
detail = np.convolve(self.z, ha) / np.sqrt(a[ptr])
ix = np.arange(int(np.round(nha)),
detail.shape[0] - int(np.round(nha)) + 1,
dtype=int)
wt[ptr, :] = detail[self.ts]
detail = detail[ix]
self.tfr[ptr, :] = detail[self.ts] * np.conj(detail[self.ts])
elif self.waveparams == 0:
for ptr in range(self.n_voices):
ha = mexhat(f[ptr])
nha = (ha.shape[0] - 1) / 2
detail = np.convolve(self.z, ha) / np.sqrt(a[ptr])
ix = np.arange(
int(np.round(nha)) + 1,
detail.shape[0] - int(np.round(nha)) + 1)
detail = detail[ix]
wt[ptr, :] = detail[self.ts]
self.tfr[ptr, :] = detail[self.ts] * np.conj(detail[self.ts])
elif isinstance(self.waveparams, np.ndarray):
rwav, cwav = self.waveparams.shape
if cwav > rwav:
self.waveparams = self.waveparams.T
wavef = np.fft.fft(self.waveparams, axis=0)
nwave = self.waveparams.shape[0]
f0 = wavef[np.abs(wavef[:nwave /
2]) == np.amax(np.abs(wavef[:nwave / 2]))]
f0 = ((f0 - 1) * (1 / nwave)).mean()
a = np.logspace(np.log10(f0 / float(self.fmin)),
np.log10(f0 / float(self.fmax)), self.n_voices)
B = 0.99
R = B / (1.001 / 2)
nscale = np.max([
128,
np.round((B * nwave * (1 + 2.0 / R) * np.log(
(1 + R / 2.0) / (1 - R / 2.0))) / 2)
])
wts = scale(self.waveparams, a, self.fmin, self.fmax, nscale)
for ptr in range(self.n_voices):
ha = wts[ptr, :]
nha = ha.shape[0] / 2
detail = np.convolve(self.z, ha) / np.sqrt(a[ptr])
detail = detail[int(np.floor(nha)):(detail.shape[0] -
np.round(nha))]
wt[ptr, :] = detail[self.ts]
self.tfr[ptr, :] = detail[self.ts] * np.conj(detail[self.ts])
# Normalization
SP = np.fft.fft(self.z, axis=0)
indmin = 1 + int(np.round(self.fmin * (self.signal.shape[0] - 2)))
indmax = 1 + int(np.round(self.fmax * (self.signal.shape[0] - 2)))
SPana = SP[indmin:(indmax + 1)]
self.tfr = np.real(self.tfr)
self.tfr = self.tfr * (np.linalg.norm(SPana)**2) / integrate_2d(
self.tfr, self.ts, f) / self.n_voices
return self.tfr, self.ts, f, wt