def plotCWT(self, order=6):
from mlpy.wavelet import cwt, autoscales, fourier_from_scales
import matplotlib.pyplot as plt
omega0 = order
#compute scales
scales = autoscales(N=self.getNumberOfSamples(), dt=self.getSamplingStep(), dj=0.05, wf='morlet', p=omega0)
spec = cwt(self.getSeries(), dt=self.getSamplingStep(), scales=scales, wf='morlet', p=omega0)
freq = fourier_from_scales(scales, 'morlet', omega0)
# approximate scales through frequencies
#freq = (omega0 + np.sqrt(2.0 + omega0**2))/(4*np.pi * scale[1:])
#get as fourier freqs
plt.figure()
ax1 = plt.subplot(211)
ax2 = plt.subplot(212, sharex=ax1)
t = np.arange( self.getNumberOfSamples() ) * self.x_step_ + self.x_start_
ax1.plot(self.getPositionVector(), self.y_, 'k')
extent=[t[0], t[-1], freq[0], freq[-1]]
img = ax2.imshow(np.abs(spec), extent=extent, aspect='auto')
#plt.colorbar(img)
plt.show()
return extent,spec
def mlpy_cwt(x, fs, filename, wv='morlet' ):
from matplotlib import pyplot as plt
import mlpy.wavelet as wave
omega0 = 0
#fs=1e6
fact=2048
t = np.arange(len(x)) / fs
#scales = wave.autoscales(N=x.shape[0], dt=1/fs, dj=0.4875, wf=wv, p=omega0)
#X = wave.cwt(x=x, dt=1/fs, scales=scales, wf=wv, p=omega0)
scales = wave.autoscales(N=x.shape[0], dt=1.0/fs, dj=.025, wf=wv, p=omega0)
X = wave.cwt(x=x, dt=1/fs, scales=scales, wf=wv, p=omega0)
fig = plt.figure(1)
ax1 = plt.subplot(2,1,1)
p1 = ax1.plot(t,x)
ax1.autoscale_view(tight=True)
ax2 = plt.subplot(2,1,2)
freq = (omega0 + np.sqrt(2.0 + omega0 ** 2)) / (4 * np.pi * scales[1:])
#print "frequencies are ", freq
freqs=[math.pow(i,-1) for i in wave.fourier_from_scales(scales, wv, omega0)]
#print "api freqs are ", freqs
p2 = ax2.imshow(np.abs(X), interpolation='nearest',aspect='auto', extent=[t[0], t[-1], freq[-1], freq[0]], vmax=abs(X).max(), vmin=-abs(X).max() )
twin_ax = ax2.twinx()
twin_ax.set_xlim(t[0], t[-1])
twin_ax.set_ylim(freq[-1], freq[0])
twin_ax.set_yscale('log')
ax2.tick_params(which='both', labelleft=False, left=False)
twin_ax.tick_params(which='both', labelleft=True, left=True, labelright=False)
#fig.colorbar(p2)
fig.savefig(filename+'_'+wv+'.pdf')
fig.clf()
def scaleogram(data, samp_rate = 100.0,wavelet = 'morlet' ,bb=6,what = 'Amp',axis = None):
"""
Computes and plots logarithmic spectrogram of the input trace.
:param data: Input data
:param sample_rate: Samplerate in Hz
:param log: True logarithmic frequency axis, False linear frequency axis
:param per_lap: Percent of overlap
:param nwin: Approximate number of windows.
:param outfile: String for the filename of output file, if None
interactive plotting is activated.
:param format: Format of image to save
:param axis: Plot into given axis, this deactivates the format and
outfile option
"""
# enforce float for samp_rate
samp_rate = float(samp_rate)
# nfft needs to be an integer, otherwise a deprecation will be raised
dscale = 0.1
dtime = 1./samp_rate
npts = data.shape[0]
tt = np.arange(0,npts/samp_rate,1/samp_rate)
xx = ml.autoscales(N=data.shape[0], dt=dtime, dj=dscale, wf=wavelet, p=bb)
X = ml.cwt(x=data, dt=dtime, scales=xx, wf=wavelet, p=bb)
freq = ml.fourier_from_scales(xx, wavelet, bb)
freq = 1./freq
# amp = X
amp = np.abs(X)
phase = np.angle(X)
if not axis:
fig = plt.figure()
ax = fig.add_subplot(111)
else:
ax = axis
ax.set_yscale('log')
if what == 'Amp':
im=ax.pcolormesh(tt,freq,amp)
else:
im=ax.pcolormesh(tt,freq,phase)
# set correct way of axis, whitespace before and after with window
# length
ax.axis('tight')
# ax.set_xlim(0, end)
ax.grid(False)
ax.set_xlabel('Time [s]')
ax.set_ylabel('Frequency [Hz]')
if axis:
return ax, im
def all_in_one(x, fs, filename, wv='morlet', nfft=2048 ):
from matplotlib import pyplot as plt
import mlpy.wavelet as wave
omega0 = 0
#fs=1e6
t = np.arange(len(x)) / fs
#scales = wave.autoscales(N=x.shape[0], dt=1/fs, dj=0.4875, wf=wv, p=omega0)
#X = wave.cwt(x=x, dt=1/fs, scales=scales, wf=wv, p=omega0)
scales = wave.autoscales(N=x.shape[0], dt=1.0/fs, dj=.025, wf=wv, p=omega0)
X = wave.cwt(x=x, dt=1/fs, scales=scales, wf=wv, p=omega0)
fig = plt.figure(1)
ax1 = plt.subplot(3,1,1)
p1 = ax1.plot(t,x)
ax1.autoscale_view(tight=True)
ax2 = plt.subplot(3,1,2)
freq = (omega0 + np.sqrt(2.0 + omega0 ** 2)) / (4 * np.pi * scales[1:])
#print "frequencies are ", freq
freqs=[math.pow(i,-1) for i in wave.fourier_from_scales(scales, wv, omega0)]
#print "api freqs are ", freqs
p2 = ax2.imshow(np.abs(X), interpolation='nearest',aspect='auto', extent=[t[0], t[-1], freq[-1], freq[0]], vmax=abs(X).max(), vmin=-abs(X).max() )
twin_ax = ax2.twinx()
twin_ax.set_xlim(t[0], t[-1])
twin_ax.set_ylim(freq[-1], freq[0])
twin_ax.set_yscale('log')
ax2.tick_params(which='both', labelleft=False, left=False)
twin_ax.tick_params(which='both', labelleft=True, left=True, labelright=False)
#fig.colorbar(p2, ax=ax2).set_label("Amplitude (dB)") #fig.colorbar(p2)
ax3 = plt.subplot(3,1,3)
wrapper = lambda fn : np.blackman(fn)
#wrapper = lambda n : np.hamming(n)
#wrapper = lambda n : np.hanning(n)
Pxx, freqs, time, im = ax3.specgram(x, NFFT=nfft, Fs=fs, detrend=pylab.detrend_none, window=wrapper(nfft), noverlap=nfft/2)
#Pxx, freqs, time, im = ax3.specgram(x, Fs=fs, NFFT=nfft)
#fig.colorbar(im, ax=ax3).set_label("Amplitude (dB)")
ax3.set_xlim(t[0], t[-1])
fig.savefig(filename+'_all'+'.pdf')
fig.clf()
def aren_wavelet(x,filename,fs):
'''
Does the same continuous wavelet transmform as the mlpy_cwt
'''
from wavelets import WaveletAnalysis
dt=1/fs
wa = WaveletAnalysis(x, dt=dt)
# wavelet power spectrum
power = wa.wavelet_power
# scales
scales = wa.scales
import mlpy.wavelet as wave
freqs=[math.pow(i,-1) for i in wave.fourier_from_scales(scales, 'morlet',2)]
# associated time vector
t = wa.time
# reconstruction of the original data
rx = wa.reconstruction()
fig, ax = plt.subplots()
T, S = np.meshgrid(t, scales)
ax.contourf(T, S, power)
#ax.set_ylim(freqs[-1],freqs[0])
#ax.set_yscale('log')
fig.savefig(filename+'.pdf')
def scaleogram(data,
samp_rate=100.0,
wavelet='morlet',
bb=6,
what='Amp',
axis=None):
"""
Computes and plots logarithmic spectrogram of the input trace.
:param data: Input data
:param sample_rate: Samplerate in Hz
:param log: True logarithmic frequency axis, False linear frequency axis
:param per_lap: Percent of overlap
:param nwin: Approximate number of windows.
:param outfile: String for the filename of output file, if None
interactive plotting is activated.
:param format: Format of image to save
:param axis: Plot into given axis, this deactivates the format and
outfile option
"""
# enforce float for samp_rate
samp_rate = float(samp_rate)
# nfft needs to be an integer, otherwise a deprecation will be raised
dscale = 0.1
dtime = 1. / samp_rate
npts = data.shape[0]
tt = np.arange(0, npts / samp_rate, 1 / samp_rate)
xx = ml.autoscales(N=data.shape[0], dt=dtime, dj=dscale, wf=wavelet, p=bb)
X = ml.cwt(x=data, dt=dtime, scales=xx, wf=wavelet, p=bb)
freq = ml.fourier_from_scales(xx, wavelet, bb)
freq = 1. / freq
# amp = X
amp = np.abs(X)
phase = np.angle(X)
if not axis:
fig = plt.figure()
ax = fig.add_subplot(111)
else:
ax = axis
ax.set_yscale('log')
if what == 'Amp':
im = ax.pcolormesh(tt, freq, amp)
else:
im = ax.pcolormesh(tt, freq, phase)
# set correct way of axis, whitespace before and after with window
# length
ax.axis('tight')
# ax.set_xlim(0, end)
ax.grid(False)
ax.set_xlabel('Time [s]')
ax.set_ylabel('Frequency [Hz]')
if axis:
return ax, im
def ratio_scaleogram(data1,data2, samp_rate = 100.0,wavelet = 'morlet' ,bb=6,what = 'Amp',axis = None):
"""
Computes and plots logarithmic spectrogram of the input trace.
:param data: Input data
:param sample_rate: Samplerate in Hz
:param log: True logarithmic frequency axis, False linear frequency axis
:param per_lap: Percent of overlap
:param nwin: Approximate number of windows.
:param outfile: String for the filename of output file, if None
interactive plotting is activated.
:param format: Format of image to save
:param axis: Plot into given axis, this deactivates the format and
outfile option
"""
# enforce float for samp_rate
samp_rate = float(samp_rate)
# nfft needs to be an integer, otherwise a deprecation will be raised
dscale = 0.05
dtime = 1./samp_rate
npts = data1.shape[0]
tt = np.arange(0,npts/samp_rate,1/samp_rate)
xx = ml.autoscales(N=data1.shape[0], dt=dtime, dj=dscale, wf=wavelet, p=bb)
X = ml.cwt(x=data1, dt=dtime, scales=xx, wf=wavelet, p=bb)
Y = ml.cwt(x=data2, dt=dtime, scales=xx, wf=wavelet, p=bb)
freq = ml.fourier_from_scales(xx, wavelet, bb)
freq = 1./freq
XY = np.abs(X*Y.conjugate())
YY = np.abs(Y*Y.conjugate())
XX = np.abs(X*X.conjugate())
ss,st = XY.shape
s = np.arange(dscale,0.6,dscale)
i= 0
Tl = bb
while i < ss:
bt = np.kaiser(Tl*(i+1),0)
XY[i,:] = np.convolve(XY[i,:],bt,'same')
XX[i,:] = np.convolve(XX[i,:],bt,'same')
YY[i,:] = np.convolve(YY[i,:],bt,'same')
i += 1
Tf = bb
i = 0
while i < st:
s = np.kaiser(Tf,0)
XY[:,i] = np.convolve(XY[:,i],s,'same')
XX[:,i] = np.convolve(XX[:,i],s,'same')
YY[:,i] = np.convolve(YY[:,i],s,'same')
i += 1
Coh = (np.abs(XY)**2)/(np.abs(XX) * np.abs(YY))
if not axis:
fig = plt.figure()
ax = fig.add_subplot(111)
else:
ax = axis
ax.set_yscale('log')
im=ax.pcolormesh(tt,freq,Coh)
# set correct way of axis, whitespace before and after with window
# length
ax.axis('tight')
# ax.set_xlim(0, end)
ax.grid(False)
ax.set_xlabel('Time [s]')
ax.set_ylabel('Frequency [Hz]')
if axis:
return ax, im
fftave = np.convolve(fft_power, np.ones(5) / 5)
# write output of fourier transform
outfile = open("fft.pow", 'w')
for i in range(0, len(fft_power)):
print >> open('fft.pow', 'a'), fft_freq[i], fft_power[i], fftave[i]
outfile = open("fft.inv", 'w')
for i in range(0, len(fkinv.real)):
print >> open('fft.inv', 'a'), fkinv.real[i]
# calculate wavelet scales
scales = wave.autoscales(N=x_pad.shape[0], dt=dt, dj=dj, wf=wf, p=p)
# convert scales to fourier periods and output
period = wave.fourier_from_scales(scales, wf=wf, p=p)
outfile = open("scales.periods", 'w')
scale_len = len(scales)
for i in range(0, scale_len):
print >> open("scales.periods",
'a'), i, scales[i], period[i], 1. / period[i]
# perform continuous wavelet transform and output
X = wave.cwt(x=x_pad, dt=dt, scales=scales, wf=wf, p=p)
power = (np.abs(X))**2.
sumpow = power.mean(axis=1)
outfile = open("sumpower.fp", 'w')
for i in range(0, scale_len):
print >> open('sumpower.fp', 'a'), sumpow[i] / xlen, period[
i], 1. / period[i], scales[i], sumpow[i] / (scales[i] * xlen)
