def draw_3D_scalogram(signal, name, draw_contours=False):
# Perform a wavelet transform on the input signal.
print "Transforming '%s' using a Morlet wavelet..." % name
transformed = Morlet(
signal,
largestscale=4,
notes=16,
scaling='log')
power_matrix = transformed.getpower()
# Downsample the image.
matrix_dimensions = numpy.shape(power_matrix)
mat_size = (matrix_dimensions[0], 1000)
power = scipy.misc.imresize(power_matrix, mat_size)
# Display the power matrix generated during the wavelet transform.
fig = pyplot.figure(name)
pyplot.title(name)
axis = fig.gca(projection='3d')
# Setup each axis' data.
f = numpy.arange(mat_size[0])
t = numpy.arange(mat_size[1])
f_major, t_major = numpy.meshgrid(f, t)
# Plot everything.
axis.plot_surface(t_major, f_major, power.transpose(), rstride=8, cstride=8, alpha=0.3)
if draw_contours:
axis.contour(t_major, f_major, power.transpose(), zdir='z', offset=0, cmap=cm.coolwarm)
axis.contour(t_major, f_major, power.transpose(), zdir='x', offset=0, cmap=cm.coolwarm)
axis.contour(t_major, f_major, power.transpose(), zdir='y', offset=0, cmap=cm.coolwarm)
axis.set_xlabel('t')
axis.set_ylabel('f')
axis.set_zlabel('amplitude')
def draw_scalogram(signal, name):
# Perform a wavelet transform on the input signal.
print "Transforming '%s' using a Morlet wavelet..." % name
transformed = Morlet(
signal,
largestscale=4,
notes=16,
scaling='log')
power_matrix = transformed.getpower()
# Display the power matrix generated during the wavelet transform.
pylab.imshow(
power_matrix,
cmap=pylab.cm.jet,
aspect='auto')
def phaseCWT(sig, Tph, dt, maxF, dF=2):
'''
Calculate Morlet wavelet transform of a signal, but as a function of
phase. Unaligned phase at the end will be discarded, and ph(t=0) must be 0,
i.e. no phase shifts!
'''
n_ph = Tph / dt
N = len(sig)
q_ph = np.floor(N / n_ph)
minF = 1. / (len(sig) / 2 * Morlet.fourierwl * dt)
F = np.linspace(minF, maxF, (maxF - minF) / dF + 1)
scales = 1 / F * 1 / Morlet.fourierwl * 1 / dt
w = Morlet(sig, scales, scaling='direct')
w_cwt_ph = np.ndarray((w.nscale, n_ph))
#import pdb; pdb.set_trace()
for sc_it in xrange(w.nscale):
w_ph = np.reshape(
np.abs(w.cwt[sc_it, :][0:q_ph * n_ph])**2, (q_ph, n_ph))
w_cwt_ph[sc_it, :] = np.mean(w_ph, 0)
sig_ph = np.reshape(sig[0:q_ph * n_ph], (q_ph, n_ph))
phases = 1. * np.arange(n_ph) / n_ph * 2 * np.pi - np.pi
return phases, w_cwt_ph, 1. / (w.scales * w.fourierwl * dt), sig_ph
def CWT(sig, dt, maxF, dF=2):
'''
Calculate a Morlet wavelet transfrom of a signal.
'''
N = len(sig)
minF = 1. / (len(sig) / 2 * Morlet.fourierwl * dt)
F = np.linspace(minF, maxF, (maxF - minF) / dF + 1)
scales = 1 / F * 1 / Morlet.fourierwl * 1 / dt
w = Morlet(sig, scales, scaling='direct')
return np.abs(w.cwt)**2, 1. / (w.scales * w.fourierwl * dt)
def getPhase(lfp, fmin, fmax, nbins, fsamp, power=False):
""" Continuous Wavelets Transform
return phase of lfp in a Tsd array
"""
import neuroseries as nts
from Wavelets import MyMorlet as Morlet
if isinstance(lfp, nts.time_series.TsdFrame):
allphase = nts.TsdFrame(lfp.index.values, np.zeros(lfp.shape))
allpwr = nts.TsdFrame(lfp.index.values, np.zeros(lfp.shape))
for i in lfp.keys():
allphase[i], allpwr[i] = getPhase(lfp[i],
fmin,
fmax,
nbins,
fsamp,
power=True)
if power:
return allphase, allpwr
else:
return allphase
elif isinstance(lfp, nts.time_series.Tsd):
cw = Morlet(lfp.values, fmin, fmax, nbins, fsamp)
cwt = cw.getdata()
cwt = np.flip(cwt, axis=0)
wave = np.abs(cwt)**2.0
phases = np.arctan2(np.imag(cwt), np.real(cwt)).transpose()
cwt = None
index = np.argmax(wave, 0)
# memory problem here, need to loop
phase = np.zeros(len(index))
for i in range(len(index)):
phase[i] = phases[i, index[i]]
phases = None
if power:
pwrs = cw.getpower()
pwr = np.zeros(len(index))
for i in range(len(index)):
pwr[i] = pwrs[index[i], i]
return nts.Tsd(lfp.index.values,
phase), nts.Tsd(lfp.index.values, pwr)
else:
return nts.Tsd(lfp.index.values, phase)
