def _phase_map(self):
self.dphi = (2*P.pi * self.nhop * P.arange(self.nfft/2+1)) / self.nfft
A = P.diff(P.angle(self.STFT),1) # Complete Phase Map
U = P.c_[P.angle(self.STFT[:,0]), A - P.atleast_2d(self.dphi).T ]
U = U - P.np.round(U/(2*P.pi))*2*P.pi
self.dPhi = U
return U
def _phase_map(self):
self.dphi = (2*P.pi * self.nhop * P.arange(self.nfft/2+1)) / self.nfft
A = P.diff(P.angle(self.STFT),1) # Complete Phase Map
U = P.c_[P.angle(self.STFT[:,0]), A - P.matrix(self.dphi).T ]
U = U - P.np.round(U/(2*P.pi))*2*P.pi
self.dPhi = U
return U
def analysis(self,x): X = stft(x,self.win,self.n) delta = pl.angle(X) - self.phs self.phs = pl.angle(X) delta = unwrap(delta) freqs = self.fc + delta*self.sr/(2*pl.pi*self.h) self.n += self.h return abs(X),freqs
def xyamb(xytab,qu,xyout=''):
mytb=taskinit.tbtool()
if not isinstance(qu,tuple):
raise Exception,'qu must be a tuple: (Q,U)'
if xyout=='':
xyout=xytab
if xyout!=xytab:
os.system('cp -r '+xytab+' '+xyout)
QUexp=complex(qu[0],qu[1])
print 'Expected QU = ',qu # , ' (',pl.angle(QUexp)*180/pi,')'
mytb.open(xyout,nomodify=False)
QU=mytb.getkeyword('QU')['QU']
P=pl.sqrt(QU[0,:]**2+QU[1,:]**2)
nspw=P.shape[0]
for ispw in range(nspw):
st=mytb.query('SPECTRAL_WINDOW_ID=='+str(ispw))
if (st.nrows()>0):
q=QU[0,ispw]
u=QU[1,ispw]
qufound=complex(q,u)
c=st.getcol('CPARAM')
fl=st.getcol('FLAG')
xyph0=pl.angle(pl.mean(c[0,:,:][pl.logical_not(fl[0,:,:])]),True)
print 'Spw = '+str(ispw)+': Found QU = '+str(QU[:,ispw]) # +' ('+str(pl.angle(qufound)*180/pi)+')'
#if ( (abs(q)>0.0 and abs(qu[0])>0.0 and (q/qu[0])<0.0) or
# (abs(u)>0.0 and abs(qu[1])>0.0 and (u/qu[1])<0.0) ):
if ( pl.absolute(pl.angle(qufound/QUexp)*180/pi)>90.0 ):
c[0,:,:]*=-1.0
xyph1=pl.angle(pl.mean(c[0,:,:][pl.logical_not(fl[0,:,:])]),True)
st.putcol('CPARAM',c)
QU[:,ispw]*=-1
print ' ...CONVERTING X-Y phase from '+str(xyph0)+' to '+str(xyph1)+' deg'
else:
print ' ...KEEPING X-Y phase '+str(xyph0)+' deg'
st.close()
QUr={}
QUr['QU']=QU
mytb.putkeyword('QU',QUr)
mytb.close()
QUm=pl.mean(QU[:,P>0],1)
QUe=pl.std(QU[:,P>0],1)
Pm=pl.sqrt(QUm[0]**2+QUm[1]**2)
Xm=0.5*atan2(QUm[1],QUm[0])*180/pi
print 'Ambiguity resolved (spw mean): Q=',QUm[0],'U=',QUm[1],'(rms=',QUe[0],QUe[1],')','P=',Pm,'X=',Xm
stokes=[1.0,QUm[0],QUm[1],0.0]
print 'Returning the following Stokes vector: '+str(stokes)
return stokes
def update_design(self):
ax = self.ax
ax.cla()
ax2 = self.ax2
ax2.cla()
wp = self.wp
ws = self.ws
gpass = self.gpass
gstop = self.gstop
b, a = ss.iirdesign(wp, ws, gpass, gstop, ftype=self.ftype, output='ba')
self.a = a
self.b = b
#b = [1,2]; a = [1,2]
#Print this on command line so we can use it in our programs
print 'b = ', pylab.array_repr(b)
print 'a = ', pylab.array_repr(a)
my_w = pylab.logspace(pylab.log10(.1*self.ws[0]), 0.0, num=512)
#import pdb;pdb.set_trace()
w, h = freqz(b, a, worN=my_w*pylab.pi)
gp = 10**(-gpass/20.)#Go from db to regular
gs = 10**(-gstop/20.)
self.design_line, = ax.plot([.1*self.ws[0], self.ws[0], wp[0], wp[1], ws[1], 1.0], [gs, gs, gp, gp, gs, gs], 'ko:', lw=2, picker=5)
ax.semilogx(w/pylab.pi, pylab.absolute(h),lw=2)
ax.text(.5,1.0, '{:d}/{:d}'.format(len(b), len(a)))
pylab.setp(ax, 'xlim', [.1*self.ws[0], 1.2], 'ylim', [-.1, max(1.1,1.1*pylab.absolute(h).max())], 'xticklabels', [])
ax2.semilogx(w/pylab.pi, pylab.unwrap(pylab.angle(h)),lw=2)
pylab.setp(ax2, 'xlim', [.1*self.ws[0], 1.2])
ax2.set_xlabel('Normalized frequency')
pylab.draw()
def _pvoc2(self, X_hat, Phi_hat=None, R=None):
"""
::
alternate (batch) implementation of phase vocoder - time-stretch
inputs:
X_hat - estimate of signal magnitude
[Phi_hat] - estimate of signal phase
[R] - resynthesis hop ratio
output:
updates self.X_hat with modified complex spectrum
"""
N, W, H = self.nfft, self.wfft, self.nhop
R = 1.0 if R is None else R
dphi = P.atleast_2d((2*P.pi * H * P.arange(N/2+1)) / N).T
print "Phase Vocoder Resynthesis...", N, W, H, R
A = P.angle(self.STFT) if Phi_hat is None else Phi_hat
U = P.diff(A,1) - dphi
U = U - P.np.round(U/(2*P.pi))*2*P.pi
t = P.arange(0,n_cols,R)
tf = t - P.floor(t)
phs = P.c_[A[:,0], U]
phs += U[:,idx[1]] + dphi # Problem, what is idx ?
Xh = (1-tf)*Xh[:-1] + tf*Xh[1:]
Xh *= P.exp( 1j * phs)
self.X_hat = Xh
def _pvoc(self, X_hat, Phi_hat=None, R=None):
"""
::
a phase vocoder - time-stretch
inputs:
X_hat - estimate of signal magnitude
[Phi_hat] - estimate of signal phase
[R] - resynthesis hop ratio
output:
updates self.X_hat with modified complex spectrum
"""
N = self.nfft
W = self.wfft
H = self.nhop
R = 1.0 if R is None else R
dphi = (2*P.pi * H * P.arange(N/2+1)) / N
print "Phase Vocoder Resynthesis...", N, W, H, R
A = P.angle(self.STFT) if Phi_hat is None else Phi_hat
phs = A[:,0]
self.X_hat = []
n_cols = X_hat.shape[1]
t = 0
while P.floor(t) < n_cols:
tf = t - P.floor(t)
idx = P.arange(2)+int(P.floor(t))
idx[1] = n_cols-1 if t >= n_cols-1 else idx[1]
Xh = X_hat[:,idx]
Xh = (1-tf)*Xh[:,0] + tf*Xh[:,1]
self.X_hat.append(Xh*P.exp( 1j * phs))
U = A[:,idx[1]] - A[:,idx[0]] - dphi
U = U - P.np.round(U/(2*P.pi))*2*P.pi
phs += (U + dphi)
t += P.randn()*P.sqrt(PVOC_VAR*R) + R # 10% variance
self.X_hat = P.np.array(self.X_hat).T
def plot_phases(in_file, plot_type, plot_log):
flags = ['histogram','phases']
plot_flag = 0
log_flag = 0
def no_log(x):
return x
fig = pylab.figure(1)
ax = fig.add_subplot(111)
try:
img = spimage.sp_image_read(in_file,0)
except:
raise IOError("Can't read %s." % in_file)
values = img.image.reshape(pylab.size(img.image))
if plot_log:
log_function = pylab.log
else:
log_function = no_log
if plot_type == PHASES:
hist = pylab.histogram(pylab.angle(values),bins=500)
ax.plot((hist[1][:-1]+hist[1][1:])/2.0,log_function(hist[0]))
elif plot_flag == HISTOGRAM:
hist = pylab.histogram2d(pylab.real(values),pylab.imag(values),bins=500)
ax.imshow(log_function(hist[0]),extent=(hist[2][0],hist[2][-1],-hist[1][-1],-hist[1][0]),interpolation='nearest')
else:
ax.plot(pylab.real(values),pylab.imag(values),'.')
return fig
def _pvoc(self, X_hat, Phi_hat=None, R=None):
"""
::
a phase vocoder - time-stretch
inputs:
X_hat - estimate of signal magnitude
[Phi_hat] - estimate of signal phase
[R] - resynthesis hop ratio
output:
updates self.X_hat with modified complex spectrum
"""
N = self.nfft
W = self.wfft
H = self.nhop
R = 1.0 if R is None else R
dphi = (2 * P.pi * H * P.arange(N / 2 + 1)) / N
print("Phase Vocoder Resynthesis...", N, W, H, R)
A = P.angle(self.STFT) if Phi_hat is None else Phi_hat
phs = A[:, 0]
self.X_hat = []
n_cols = X_hat.shape[1]
t = 0
while P.floor(t) < n_cols:
tf = t - P.floor(t)
idx = P.arange(2) + int(P.floor(t))
idx[1] = n_cols - 1 if t >= n_cols - 1 else idx[1]
Xh = X_hat[:, idx]
Xh = (1 - tf) * Xh[:, 0] + tf * Xh[:, 1]
self.X_hat.append(Xh * P.exp(1j * phs))
U = A[:, idx[1]] - A[:, idx[0]] - dphi
U = U - P.np.round(U / (2 * P.pi)) * 2 * P.pi
phs += (U + dphi)
t += P.randn() * P.sqrt(PVOC_VAR * R) + R # 10% variance
self.X_hat = P.np.array(self.X_hat).T
def plot_phases(in_file, plot_type, plot_log):
plot_flag = 0
def no_log(x):
return x
fig = pylab.figure(1)
ax = fig.add_subplot(111)
try:
img = spimage.sp_image_read(in_file, 0)
except IOError:
raise IOError("Can't read %s." % in_file)
values = img.image.reshape(pylab.size(img.image))
if plot_log:
log_function = pylab.log
else:
log_function = no_log
if plot_type == PHASES:
hist = pylab.histogram(pylab.angle(values), bins=500)
ax.plot((hist[1][:-1] + hist[1][1:]) / 2, log_function(hist[0]))
elif plot_flag == HISTOGRAM:
hist = pylab.histogram2d(pylab.real(values),
pylab.imag(values),
bins=500)
ax.imshow(log_function(hist[0]),
extent=(hist[2][0], hist[2][-1], -hist[1][-1], -hist[1][0]),
interpolation='nearest')
else:
ax.plot(pylab.real(values), pylab.imag(values), '.')
return fig
def _pvoc2(self, X_hat, Phi_hat=None, R=None):
"""
::
alternate (batch) implementation of phase vocoder - time-stretch
inputs:
X_hat - estimate of signal magnitude
[Phi_hat] - estimate of signal phase
[R] - resynthesis hop ratio
output:
updates self.X_hat with modified complex spectrum
"""
N, W, H = self.nfft, self.wfft, self.nhop
R = 1.0 if R is None else R
dphi = P.atleast_2d((2 * P.pi * H * P.arange(N / 2 + 1)) / N).T
print("Phase Vocoder Resynthesis...", N, W, H, R)
A = P.angle(self.STFT) if Phi_hat is None else Phi_hat
U = P.diff(A, 1) - dphi
U = U - P.np.round(U / (2 * P.pi)) * 2 * P.pi
t = P.arange(0, n_cols, R)
tf = t - P.floor(t)
phs = P.c_[A[:, 0], U]
phs += U[:, idx[1]] + dphi # Problem, what is idx ?
Xh = (1 - tf) * Xh[:-1] + tf * Xh[1:]
Xh *= P.exp(1j * phs)
self.X_hat = Xh
def _istftm(self, X_hat=None, Phi_hat=None, pvoc=False, usewin=True, resamp=None):
"""
::
Inverse short-time Fourier transform magnitude. Make a signal from a |STFT| transform.
Uses phases from self.STFT if Phi_hat is None.
Inputs:
X_hat - N/2+1 magnitude STFT [None=abs(self.STFT)]
Phi_hat - N/2+1 phase STFT [None=exp(1j*angle(self.STFT))]
pvoc - whether to use phase vocoder [False]
usewin - whether to use overlap-add [False]
Returns:
x_hat - estimated signal
"""
if not self._have_stft:
return None
X_hat = P.np.abs(self.STFT) if X_hat is None else P.np.abs(X_hat)
if pvoc:
self._pvoc(X_hat, Phi_hat, pvoc)
else:
Phi_hat = P.angle(self.STFT) if Phi_hat is None else Phi_hat
self.X_hat = X_hat * P.exp( 1j * Phi_hat )
if usewin:
self.win = P.hanning(self.nfft)
self.win *= 1.0 / ((float(self.nfft)*(self.win**2).sum())/self.nhop)
else:
self.win = P.ones(self.nfft)
if resamp:
self.win = sig.resample(self.win, int(P.np.round(self.nfft * resamp)))
fp = self._check_feature_params()
self.x_hat = self._overlap_add(P.real(self.nfft * P.irfft(self.X_hat.T)), usewin=usewin, resamp=resamp)
if self.verbosity:
print "Extracted iSTFTM->self.x_hat"
return self.x_hat
def _istftm(self,
X_hat=None,
Phi_hat=None,
pvoc=False,
usewin=True,
resamp=None):
"""
::
Inverse short-time Fourier transform magnitude. Make a signal from a |STFT| transform.
Uses phases from self.STFT if Phi_hat is None.
Inputs:
X_hat - N/2+1 magnitude STFT [None=abs(self.STFT)]
Phi_hat - N/2+1 phase STFT [None=exp(1j*angle(self.STFT))]
pvoc - whether to use phase vocoder [False]
usewin - whether to use overlap-add [False]
Returns:
x_hat - estimated signal
"""
if not self._have_stft:
return None
X_hat = self.X if X_hat is None else P.np.abs(X_hat)
if pvoc:
self._pvoc(X_hat, Phi_hat, pvoc)
else:
Phi_hat = P.angle(self.STFT) if Phi_hat is None else Phi_hat
self.X_hat = X_hat * P.exp(1j * Phi_hat)
if usewin:
if self.win is None:
self.win = P.ones(
self.wfft) if self.window == 'rect' else P.np.sqrt(
P.hanning(self.wfft))
if len(self.win) != self.nfft:
self.win = P.r_[self.win, P.np.zeros(self.nfft - self.wfft)]
if len(self.win) != self.nfft:
error.BregmanError(
"features_base.Features._istftm(): assertion failed len(self.win)==self.nfft"
)
else:
self.win = P.ones(self.nfft)
if resamp:
self.win = sig.resample(self.win,
int(P.np.round(self.nfft * resamp)))
fp = self._check_feature_params()
self.x_hat = self._overlap_add(P.real(P.irfft(self.X_hat.T)),
usewin=usewin,
resamp=resamp)
if self.verbosity:
print("Extracted iSTFTM->self.x_hat")
return self.x_hat
def _icqft(self, V_hat):
"""
::
Inverse constant-Q Fourier transform. Make a signal from a constant-Q transform.
"""
if not self._have_cqft:
return False
fp = self._check_feature_params()
X_hat = pylab.array( pylab.dot(self.Q.T, V_hat) ) * pylab.exp( 1j * pylab.angle(self.STFT) )
self.x_hat = self._overlap_add( pylab.real(fp['nfft'] * pylab.irfft(X_hat.T)) )
if fp['verbosity']:
print "Extracted iCQFT->x_hat"
return True
def plot_image(in_file,*arguments):
try:
img = spimage.sp_image_read(in_file,0)
except:
print "Error: %s is not a readable .h5 file\n" % in_file
plot_flags = ['abs','mask','phase','real','imag']
shift_flags = ['shift']
log_flags = ['log']
plot_flag = 0
shift_flag = 0
log_flag = 0
for flag in arguments:
flag = flag.lower()
if flag in plot_flags:
plot_flag = flag
elif flag in shift_flags:
shift_flag = flag
elif flag in log_flags:
log_flag = flag
else:
print "unknown flag %s" % flag
if shift_flag:
img = spimage.sp_image_shift(img)
def no_log(x):
return x
if log_flag:
log_function = pylab.log
else:
log_function = no_log
if (plot_flag == "mask"):
pylab.imshow(img.mask,origin='lower',interpolation="nearest")
elif(plot_flag == "phase"):
pylab.imshow(pylab.angle(img.image),cmap='hsv',origin='lower',interpolation="nearest")
elif(plot_flag == "real"):
pylab.imshow(log_function(pylab.real(img.image)),origin='lower',interpolation="nearest")
elif(plot_flag == "imag"):
pylab.imshow(log_function(pylab.imag(img.image)),origin='lower',interpolation="nearest")
else:
pylab.imshow(log_function(abs(img.image)),origin='lower',interpolation="nearest")
pylab.show()
def _istftm(self, X_hat, Phi_hat=None):
"""
::
Inverse short-time Fourier transform magnitude. Make a signal from a |STFT| transform.
Uses phases from self.STFT if Phi_hat is None.
"""
if not self._have_stft:
return False
if Phi_hat is None:
Phi_hat = pylab.exp( 1j * pylab.angle(self.STFT))
fp = self._check_feature_params()
X_hat = X_hat * Phi_hat
self.x_hat = self._overlap_add( pylab.real(fp['nfft'] * pylab.irfft(X_hat.T)) )
if fp['verbosity']:
print "Extracted iSTFTM->self.x_hat"
return True
def _istftm(self, X_hat=None, Phi_hat=None, pvoc=False, usewin=True, resamp=None):
"""
::
Inverse short-time Fourier transform magnitude. Make a signal from a |STFT| transform.
Uses phases from self.STFT if Phi_hat is None.
Inputs:
X_hat - N/2+1 magnitude STFT [None=abs(self.STFT)]
Phi_hat - N/2+1 phase STFT [None=exp(1j*angle(self.STFT))]
pvoc - whether to use phase vocoder [False]
usewin - whether to use overlap-add [False]
Returns:
x_hat - estimated signal
"""
if not self._have_stft:
return None
X_hat = self.X if X_hat is None else P.np.abs(X_hat)
if pvoc:
self._pvoc(X_hat, Phi_hat, pvoc)
else:
Phi_hat = P.angle(self.STFT) if Phi_hat is None else Phi_hat
self.X_hat = X_hat * P.exp(1j * Phi_hat)
if usewin:
if self.win is None:
self.win = P.ones(self.wfft) if self.window == 'rect' else P.np.sqrt(
P.hanning(self.wfft))
if len(self.win) != self.nfft:
self.win = P.r_[self.win, P.np.zeros(self.nfft - self.wfft)]
if len(self.win) != self.nfft:
error.BregmanError(
"features_base.Features._istftm(): assertion failed len(self.win)==self.nfft")
else:
self.win = P.ones(self.nfft)
if resamp:
self.win = sig.resample(
self.win, int(P.np.round(self.nfft * resamp)))
fp = self._check_feature_params()
self.x_hat = self._overlap_add(
P.real(P.irfft(self.X_hat.T)), usewin=usewin, resamp=resamp)
if self.verbosity:
print("Extracted iSTFTM->self.x_hat")
return self.x_hat
def calc_phase(self):
self.s = (fourier.rb_fft_1d(self.r, undersampling=0, fft_shift_flag=1)).T
# self.s = self.s.T
self.abs_array = abs(self.s)
self.phase_array = pylab.angle(self.s)
for i in range(0, np.shape(self.phase_array)[0]):
for j in range(0, np.shape(self.phase_array)[1]):
self.phase_array[i][j] = self.phase_array[i][j]*180/np.pi
n_i=np.shape(self.r)[0]
n_t=np.shape(self.r)[1]
#calculate the frequency axis
self.s_axis[0]=np.fft.fftfreq(n_t, 3e8*100*2.11e-15)
self.s_axis[0]=self.s_axis[0][:n_t/2]
self.i_max=self.abs_array[0].argmax()
print("Frequency, rough guess:", self.s_axis[0][self.i_max])
#now refine this by weighted averaging???
#this function is general, but it assumes that s[0] is the best interferogram
w0=np.average(self.s_axis[0][self.i_max-2:self.i_max+3], weights=self.abs_array[0][self.i_max-2:self.i_max+3])
print("Frequency, refined guess:", w0)
tau=1/(w0*3e8*100e-15)
#now find the phases at the i_max and the point before and after
i_fit=list(range(self.i_max-1, self.i_max+2)) #these are three points
ph=np.zeros(n_i)
for j in range(0, n_i):
ph[j]=np.average(self.phase_array[j][i_fit])
print(ph[0], ph[1])
simple_phase= (ph[0] - ph[1])
print(simple_phase)
def _calculatefdData(self,tdData):
#no need to copy it before (access member variable is ugly but shorter)
#calculate the fft of the X channel
fd=py.fft(tdData.getEX())
#calculate absolute and phase values
fdabs=abs(fd)
fdph=abs(py.unwrap(py.angle(fd)))
#calculate frequency axis
dfreq=py.fftfreq(tdData.num_points,tdData.dt)
#extrapolate phase to 0 and 0 frequency
fdph=self.removePhaseOffset(dfreq,fdph)
#set up the fdData array
t=py.column_stack((dfreq,fd.real,fd.imag,fdabs,fdph))
#this is so not nice!
self.fdData=t
unc=self.calculateFDunc()
t=self.getcroppedData(t,0,unc[-1,0])
#interpolate uncertainty
intpunc=interp1d(unc[:,0],unc[:,1:],axis=0)
unc=intpunc(t[:,0])
return py.column_stack((t,unc))
for flag in arguments:
if flag in flags:
plot_flag = flag
elif flag in log_flags:
log_flag = flag
else:
print "unknown flag %s" % flag
if log_flag == 'log':
log_function = pylab.log
else:
log_function = no_log
if plot_flag == 'phases':
hist = pylab.histogram(pylab.angle(values),bins=50)
ax.plot((hist[1][:-1]+hist[1][1:])/2.0,log_function(hist[0]))
elif plot_flag == 'histogram':
hist = pylab.histogram2d(pylab.real(values),pylab.imag(values),bins=500)
ax.imshow(log_function(hist[0]),extent=(hist[2][0],hist[2][-1],-hist[1][-1],-hist[1][0]),interpolation='nearest')
else:
ax.plot(pylab.real(values),pylab.imag(values),'.')
return fig
if __name__ == "__main__":
try:
plot_phases(sys.argv[1],*sys.argv[2:])
pylab.show()
except:
pi = pl.pi
sig = pl.cos(2 * pi * 5 * t / T) + pl.sin(
2 * pi * 15 * t / T) + pl.cos(2 * pi * 10 * t / T - pl.pi / 4)
spec = dft(sig)
pl.figure(figsize=(10, 5))
pl.subplot(221)
pl.title('Real (cosines)')
pl.ylim(-1, 1)
pl.stem(t, spec.real, 'k-', linewidth=1)
pl.subplot(222)
pl.title('Imaginary (sines)')
pl.ylim(-1, 1)
pl.stem(t, spec.imag, 'k-', linewidth=1)
pl.subplot(223)
pl.title('Magnitudes')
pl.ylim(0, 1.1)
pl.stem(t, abs(spec), 'k-', linewidth=1)
pl.subplot(224)
pl.title('Phases')
pl.ylim(0, 1.1)
j = 0
for i in abs(spec):
if abs(i) < 0.1: spec[j] = 0 + 0j
j += 1
pl.stem(t, pl.angle(spec), 'k-', linewidth=1)
pl.ylim(-pi, pi)
pl.tight_layout()
pl.show()
def calculateinitsunc(self,H,l,sigma_L = 1e-6,sigma_Theta = 1,n_exact = 1,filename=None):
# Calculates the uncertianty on n and k according to:
# W. Withayachumnankul, B. M. Fisher, H. Lin, D. Abbott, "Uncertainty in terahertz time-domain spectroscopy measurement", J. Opt. Soc. Am. B., Vol. 25, No. 6, June 2008, pp. 1059-1072
#
# sigma_L = standard uncertainty on sample thickness in meter
# sigma_Theta = interval of sample misallignment in degree
# n_exact = exact value of the refractive index of air during the measurements
n, k = self.calculateinits(H,l)
n = py.asarray(n)
k = py.asarray(k)
Asam = []
Aref = []
Bsam = []
Bref = []
for i in range(len(self.H.getfreqs())):
Asam.append((py.sum(py.imag(self.H.fdsam.getFAbs().tolist()[i]*py.exp(1j*2*py.pi*self.H.getfreqs().tolist()[i]*self.H.fdsam._tdData.getTimes()))*self.H.fdsam._tdData.getUncEX())**2))
Aref.append((py.sum(py.imag(self.H.fdref.getFAbs().tolist()[i]*py.exp(1j*2*py.pi*self.H.getfreqs().tolist()[i]*self.H.fdref._tdData.getTimes()))*self.H.fdref._tdData.getUncEX())**2))
Bsam.append((py.sum(py.real(self.H.fdsam.getFAbs().tolist()[i]*py.exp(1j*2*py.pi*self.H.getfreqs().tolist()[i]*self.H.fdsam._tdData.getTimes()))*self.H.fdsam._tdData.getUncEX())**2))
Bref.append((py.sum(py.real(self.H.fdref.getFAbs().tolist()[i]*py.exp(1j*2*py.pi*self.H.getfreqs().tolist()[i]*self.H.fdref._tdData.getTimes()))*self.H.fdref._tdData.getUncEX())**2))
# Uncertainty on n
sn_Esam_2 = ((c/(2*py.pi*self.H.getfreqs()*l))**2 * py.asarray(Asam)/self.H.fdsam.getFAbs()**4)/self.H.fdsam._tdData.numberOfDataSets
sn_Eref_2 = ((c/(2*py.pi*self.H.getfreqs()*l))**2 * py.asarray(Aref)/self.H.fdref.getFAbs()**4)/self.H.fdref._tdData.numberOfDataSets
sn_l_2 = ((n-self.n_0)*sigma_L/l)**2
#sn_l_2_1 = (c*self.H.getFPh()/(2*py.pi*self.H.getfreqs()*l*l))**2 * sigma_L**2
#sn_H_2 = (c/(2*py.pi*self.H.getfreqs()*l))**2 * self.H.getFPhUnc()**2
fn_Theta = (n-self.n_0.real)*(1/py.cos(sigma_Theta*py.pi/180)-1)
fn_H = (c/(2*py.pi*self.H.getfreqs()*l))*py.absolute(-py.angle(4*(n-1j*k)*self.n_0/(n-1j*k+self.n_0)**2))
fn_FP = (c/(2*py.pi*self.H.getfreqs()*l))*py.absolute(-py.angle(1/(1-((n-1j*k-self.n_0)/(n-1j*k+self.n_0))**2*py.exp(-2*1j*(n-1j*k)*2*py.pi*self.H.getfreqs()*l/c))))
fn_n0 = abs(self.n_0.real - n_exact)*py.ones(len(self.H.getFPh()))
u_n = py.sqrt(sn_l_2+sn_Esam_2+sn_Eref_2)+fn_Theta+fn_H+fn_FP+fn_n0
# Uncertianty on k
sk_Esam_2 = ((c/(2*py.pi*self.H.getfreqs()*l))**2 *(Bsam/self.H.fdsam.getFAbs()**4 + ((n-self.n_0)/(n+self.n_0))**2 * sn_Esam_2/n**2))/self.H.fdsam._tdData.numberOfDataSets
sk_Eref_2 = ((c/(2*py.pi*self.H.getfreqs()*l))**2 *(Bref/self.H.fdref.getFAbs()**4 + ((n-self.n_0)/(n+self.n_0))**2 * sn_Eref_2/n**2))/self.H.fdref._tdData.numberOfDataSets
sk_l_2 = (k*sigma_L/l)**2 + (c*(n-self.n_0)/((n+self.n_0)*n*2*py.pi*self.H.getfreqs()*l))**2*sn_l_2
#sk_l_2_1 = ((c/(2*py.pi*self.H.getfreqs()*l*l))*py.log(self.H.getFAbs()*(n+self.n_0.real)**2/(4*n*self.n_0.real)))**2 * sigma_L**2
#sk_H_2 = (-c/(2*py.pi*self.H.getfreqs()*l*self.H.getFAbs()))**2 * self.H.getFAbsUnc()**2
fk_Theta = k*(1/py.cos(sigma_Theta*py.pi/180)-1)+c*(n-self.n_0.real)*fn_Theta/(n*2*py.pi*self.H.getfreqs()*l*(n+self.n_0.real))
fk_H = (c/(2*py.pi*self.H.getfreqs()*l))*(py.log(py.absolute(n/(n-1j*k)*((n-1j*k+self.n_0.real)/(n+self.n_0.real))**2))+py.absolute(fn_H)*(n-self.n_0.real)/(n*(n+self.n_0.real)))
fk_FP = (c/(2*py.pi*self.H.getfreqs()*l))*(py.absolute(-py.log(py.absolute(1/(1-((n-1j*k-self.n_0)/(n-1j*k+self.n_0))**2*py.exp(-2*1j*(n-1j*k)*2*py.pi*self.H.getfreqs()*l/c)))))+py.absolute(fn_FP)*(n-self.n_0.real)/(n*(n+self.n_0.real)))
fk_n0 = (c/(2*py.pi*self.H.getfreqs()*l))*(n-self.n_0.real)*(self.n_0.real - n_exact)/(n*self.n_0.real)
u_k = py.sqrt(sk_l_2+sk_Esam_2+sk_Eref_2)+fk_Theta+fk_H+fk_FP+fk_n0
# Convert n in epsilon Epsilon = Epsilon_1 + j Epsilon_2 = (n+jk)**2
# Epsilon_1 = n**2 - k**2
# Epsilon_2 = -2nk
Epsilon_1 = n**2 - k **2
Epsilon_2 = -2 * n * k
u_Epsilon_1 = py.sqrt((2*n*u_n)**2 + (-2*k*u_k)**2)
u_Epsilon_2 = py.sqrt((-2*k*u_n)**2 + (-2*n*u_k)**2)
# Calculate absorption coefficient
# alpha = 4 * pi * k * f / c1
alpha = 4 * py.pi * k * self.H.getfreqs() / (100 * c) # in cm^-1
u_alpha = 4 * py.pi * u_k * self.H.getfreqs() / (100 * c) # in cm^-1
# Calculate maximum measurable absorption coefficient according to
# P. U. Jepsen and B. M. Fisher: "Dynamic Range in terahertz time-domain transmission and reflection spectroscopy", Optics Letters, Vol. 30, n. 1, pp. 29-31, Jan 2005
alpha_max = 2 * py.log((self.H.fdsam.getDR() * 4 * n)/(n + 1)**2) / (100 * l) # in cm^-1
# Save results into a table accessible from outside
self.n_with_unc=py.real(py.column_stack((
self.H.getfreqs(), # frequencies
n, k, # real and imaginary part of n
u_n, u_k, # k=1 combined uncertainty on n and k
py.sqrt(sn_l_2), py.sqrt(sn_Esam_2), py.sqrt(sn_Eref_2), fn_Theta, fn_H, fn_FP, fn_n0, # Uncertainty components of n due to thickness, H, sample misallignment, k<<<, Neglect FP, ref ind of air
py.sqrt(sk_l_2), py.sqrt(sk_Esam_2), py.sqrt(sk_Eref_2), fk_Theta, fk_H, fk_FP, fk_n0, # Uncertainty components of k due to thickness, H, sample misallignment, k<<<, Neglect FP, ref ind of air
Epsilon_1, Epsilon_2, # Real and imaginary part of Epsilon
u_Epsilon_1, u_Epsilon_2, # k = 1 uncertainty on the real and imaginary part of Epsilon
alpha, u_alpha, # Absorption coefficient and its k = 1 uncertainty
alpha_max, # Maximum measurable absorption coefficient
)))
return
return sig/N
def dft(s):
N = len(s)
out = pl.zeros(N)*1j;
for k in range(0,N):
for t in range(0,N):
out[k] += s[t]*(pl.cos(2*pl.pi*k*t/N)
- 1j*pl.sin(2*pl.pi*k*t/N))
return out/N
T = 100
saw = pl.zeros(T)
t = pl.arange(0,T)
N = T // 2
for k in range(1,N):
saw += (1/k)*pl.sin(2*pl.pi*k*t/T)
saw += 0.001 + 0.001*pl.cos(pl.pi*t/T)
saw *= 2/(pl.pi)
spec = dft(saw)
print(abs(spec[0]))
phs = pl.angle(spec)
pl.figure(figsize=(8,3))
pl.stem(t,phs, 'k-', linewidth=1)
pl.ylim(-pl.pi-0.5, +pl.pi+0.5)
pl.tight_layout()
pl.show()
def xyamb(xytab, qu, xyout=''):
mytb = taskinit.tbtool()
if not isinstance(qu, tuple):
raise Exception, 'qu must be a tuple: (Q,U)'
if xyout == '':
xyout = xytab
if xyout != xytab:
os.system('cp -r ' + xytab + ' ' + xyout)
QUexp = complex(qu[0], qu[1])
print 'Expected QU = ', qu # , ' (',pl.angle(QUexp)*180/pi,')'
mytb.open(xyout, nomodify=False)
QU = mytb.getkeyword('QU')['QU']
P = pl.sqrt(QU[0, :]**2 + QU[1, :]**2)
nspw = P.shape[0]
for ispw in range(nspw):
st = mytb.query('SPECTRAL_WINDOW_ID==' + str(ispw))
if (st.nrows() > 0):
q = QU[0, ispw]
u = QU[1, ispw]
qufound = complex(q, u)
c = st.getcol('CPARAM')
fl = st.getcol('FLAG')
xyph0 = pl.angle(pl.mean(c[0, :, :][pl.logical_not(fl[0, :, :])]),
True)
print 'Spw = ' + str(ispw) + ': Found QU = ' + str(
QU[:, ispw]) # +' ('+str(pl.angle(qufound)*180/pi)+')'
#if ( (abs(q)>0.0 and abs(qu[0])>0.0 and (q/qu[0])<0.0) or
# (abs(u)>0.0 and abs(qu[1])>0.0 and (u/qu[1])<0.0) ):
if (pl.absolute(pl.angle(qufound / QUexp) * 180 / pi) > 90.0):
c[0, :, :] *= -1.0
xyph1 = pl.angle(
pl.mean(c[0, :, :][pl.logical_not(fl[0, :, :])]), True)
st.putcol('CPARAM', c)
QU[:, ispw] *= -1
print ' ...CONVERTING X-Y phase from ' + str(
xyph0) + ' to ' + str(xyph1) + ' deg'
else:
print ' ...KEEPING X-Y phase ' + str(xyph0) + ' deg'
st.close()
QUr = {}
QUr['QU'] = QU
mytb.putkeyword('QU', QUr)
mytb.close()
QUm = pl.mean(QU[:, P > 0], 1)
QUe = pl.std(QU[:, P > 0], 1)
Pm = pl.sqrt(QUm[0]**2 + QUm[1]**2)
Xm = 0.5 * atan2(QUm[1], QUm[0]) * 180 / pi
print 'Ambiguity resolved (spw mean): Q=', QUm[0], 'U=', QUm[
1], '(rms=', QUe[0], QUe[1], ')', 'P=', Pm, 'X=', Xm
stokes = [1.0, QUm[0], QUm[1], 0.0]
print 'Returning the following Stokes vector: ' + str(stokes)
return stokes
ti = int(ts*H)
scal = 3*D/4
def plock(phs):
N = len(phs)
x = p2r(pl.ones(N),phs)
y = pl.zeros(N)+0j
y[0], y[N-1] = x[0], x[N-1]
for i in range(1,N-1):
y[i] = x[i] - (x[i-1] + x[i+1])
return y
for n in range(0,L-(N+H),ti):
X1 = stft(signal[n:n+N],win)
X2 = stft(signal[n+H:n+H+N],win)
diffs = pl.angle(X2) - pl.angle(X1)
phs += diffs
Y = p2r(abs(X2),phs)
output[np:np+N] += istft(Y,win)
phs = pl.angle(plock(phs))
np += H
output = pl.array(output*zdbfs/scal,dtype='int16')
wf.write(sys.argv[3],sr,output)
import os
try:
os.spawnlp(os.P_WAIT, 'sndfile-play', 'sndfile-play', sys.argv[3])
except:
pass
L2 = len(in2)
if L2 > L1: L = L2
else: L = L1
signal1 = pl.zeros(L)
signal2 = pl.zeros(L)
signal1[:len(in1)] = in1 / zdbfs
signal2[:len(in2)] = in2 / zdbfs
output = pl.zeros(L)
win = pl.hanning(N)
scal = 1.5 * D / 4
for n in range(0, L, H):
if (L - n < N): break
frame1 = stft(signal1[n:n + N], win, n)
frame2 = stft(signal2[n:n + N], win, n)
mags = abs(frame1)
env1 = spec_env(frame1, 20)
env2 = spec_env(frame2, 20)
phs = pl.angle(frame1)
if (min(env1) > 0):
frame = p2r(mags * env2 / env1, phs)
else:
frame = p2r(mags * env2, phs)
output[n:n + N] += istft(frame, win, n)
a = max(signal1)
b = max(output)
c = a / b
output = pl.array(output * zdbfs * c / scal, dtype='int16')
wf.write(sys.argv[3], sr, output)
H = N//D
zdbfs = 32768
(sr,signal) = wf.read(sys.argv[2])
signal = signal/zdbfs
L = len(signal)
win = pl.hanning(N)
phs = pl.zeros(N//2+1)
np = 0
ts = float(sys.argv[1])
output = pl.zeros(int(L/ts)+N)
ti = int(ts*H)
scal = 3*D/4
for n in range(0,L-(N+H),ti):
X1 = stft(signal[n:n+N],win)
X2 = stft(signal[n+H:n+H+N],win)
diffs = pl.angle(X2) - pl.angle(X1)
phs += diffs
Y = p2r(abs(X2),phs)
output[np:np+N] += istft(Y,win)
np += H
output = pl.array(output*zdbfs/scal,dtype='int16')
wf.write(sys.argv[3],sr,output)
import os
try:
os.spawnlp(os.P_WAIT, 'sndfile-play', 'sndfile-play', sys.argv[3])
except:
pass
