def make_unitary(self):
fft_val = np.fft(self.v)
fft_imag = fft_val.imag
fft_real = fft_val.real
fft_norms = [sqrt(fft_imag[n]**2 + fft_real[n]**2) for n in range(len(self.v))]
fft_unit = fft_val / fft_norms
self.v = (np.ifft(fft_unit)).real
def shift(x, n):
vec1 = 0 * x
vec1[n] = 1
vec1fft = np.fft(vec1)
xft = np.fft(x)
return np.real(np.ifft(xft * vec1fft))
def fourier_projection(self, density):
ft_density = np.fft(density)
# -m wraps around array, but that should be OK....
# --> self._A_ell_expt[l] is shape (2l+1) x n_q = (m x q)
# ft_coefficients[:,l,:] is shape n_q x (2l+1) = (q x m) (tranposed later)
ft_coefficients = self._sph_harm_projector(ft_density)
# zero out the array, use it to store the next iter
ft_density[:,:,:] = 0.0 + 1j * 0.0
for l in range(self.order_cutoff):
A_ell_model = ft_coefficients[:,l,:].T # (2l+1) x n_q = (m x q)
# find U that rotates the experimental vectors into as close
# agreement as possible as the model vectors
U = math2.kabsch(self._A_ell_expt[l], A_ell_model)
# update: k --> k+1
A_ell_prime = np.dot(self._A_ell_expt[l], U)
ft_density_prime += self._sph_harm_projector.expand_sph_harm_order(A_ell_prime, l)
updated_density = np.ifft(ft_density)
return updated_density
def make_unitary(self):
fft_val = np.fft(self.v)
fft_imag = fft_val.imag
fft_real = fft_val.real
fft_norms = [
sqrt(fft_imag[n]**2 + fft_real[n]**2) for n in range(len(self.v))
]
fft_unit = fft_val / fft_norms
self.v = (np.ifft(fft_unit)).real
def idct(v,axis=-1):
n = len(v.shape)
N = v.shape[axis]
even = (N%2 == 0)
slices = [None]*4
for k in range(4):
slices[k] = []
for j in range(n):
slices[k].append(slice(None))
k = np.arange(N)
if even:
ak = np.r_[1.0,[2]*(N-1)]*np.exp(1j*pi*k/(2*N))
newshape = np.ones(n)
newshape[axis] = N
ak.shape = newshape
xhat = np.real(np.ifft(v*ak,axis=axis))
x = 0.0*v
slices[0][axis] = slice(None,None,2)
slices[1][axis] = slice(None,N/2)
slices[2][axis] = slice(N,None,-2)
slices[3][axis] = slice(N/2,None)
for k in range(4):
slices[k] = tuple(slices[k])
x[slices[0]] = xhat[slices[1]]
x[slices[2]] = xhat[slices[3]]
return x
else:
ak = 2*np.exp(1j*pi*k/(2*N))
newshape = np.ones(n)
newshape[axis] = N
ak.shape = newshape
newshape = list(v.shape)
newshape[axis] = 2*N
Y = zeros(newshape,np.complex128)
#Y[:N] = ak*v
#Y[(N+1):] = conj(Y[N:0:-1])
slices[0][axis] = slice(None,N)
slices[1][axis] = slice(None,None)
slices[2][axis] = slice(N+1,None)
slices[3][axis] = slice((N-1),0,-1)
Y[slices[0]] = ak*v
Y[slices[2]] = conj(Y[slices[3]])
x = np.real(np.ifft(Y,axis=axis))[slices[0]]
return x
def idct(v,axis=-1):
n = len(v.shape)
N = v.shape[axis]
even = (N%2 == 0)
slices = [None]*4
for k in range(4):
slices[k] = []
for j in range(n):
slices[k].append(slice(None))
k = np.arange(N)
if even:
ak = np.r_[1.0,[2]*(N-1)]*np.exp(1j*pi*k/(2*N))
newshape = np.ones(n)
newshape[axis] = N
ak.shape = newshape
xhat = np.real(np.ifft(v*ak,axis=axis))
x = 0.0*v
slices[0][axis] = slice(None,None,2)
slices[1][axis] = slice(None,N/2)
slices[2][axis] = slice(N,None,-2)
slices[3][axis] = slice(N/2,None)
for k in range(4):
slices[k] = tuple(slices[k])
x[slices[0]] = xhat[slices[1]]
x[slices[2]] = xhat[slices[3]]
return x
else:
ak = 2*np.exp(1j*pi*k/(2*N))
newshape = np.ones(n)
newshape[axis] = N
ak.shape = newshape
newshape = list(v.shape)
newshape[axis] = 2*N
Y = zeros(newshape,np.complex128)
#Y[:N] = ak*v
#Y[(N+1):] = conj(Y[N:0:-1])
slices[0][axis] = slice(None,N)
slices[1][axis] = slice(None,None)
slices[2][axis] = slice(N+1,None)
slices[3][axis] = slice((N-1),0,-1)
Y[slices[0]] = ak*v
Y[slices[2]] = conj(Y[slices[3]])
x = np.real(np.ifft(Y,axis=axis))[slices[0]]
return x
def conv(x,y):
x1=np.zeros(x.size)
x1[0:x.size]=x #added zeros
y1=np.zeros(y.size)
y1[0:y.size]=y #added zeros
x1ft=np.fft(x1)
y1ft=np.fft(y1)
vect1=np.real(np.ifft(x1ft*y1ft))
return vect1[0:x.size]
def conv(x, y):
x1 = np.zeros(x.size)
x1[0:x.size] = x #added zeros
y1 = np.zeros(y.size)
y1[0:y.size] = y #added zeros
x1ft = np.fft(x1)
y1ft = np.fft(y1)
vect1 = np.real(np.ifft(x1ft * y1ft))
return vect1[0:x.size]
def smoothGaussian1dMirror(array,sigma):
array_reversed = list(array.copy())
array_reversed.reverse()
array_reversed = numpy.array(array_reversed)
array_mirrored = numpy.zeros(2*len(array))
array_mirrored[:len(array)] = array[:]
array_mirrored[len(array):] = array_reversed[:]
array_smoothed = numpy.ifft(numpy.fft(array_mirrored)*1/numpy.sqrt(2*numpy.pi)/sigma*numpy.exp(numpy.arange(0,len(array_mirrored),1.0)**2/2.0/sigma**2) )
array_smoothed = array_smoothed[:len(array)]
print array_smoothed
return array_smoothed
def correlationFunctionByFFT3D(box,nbin,Lcell=1.0):
""" use FFT """
#fft to get k-space box
kbox=np.fftn(box)
#from k-space box get power spectrum
pk=1
#ifft to get correlation function
rbox=np.ifft(pk)
return rbox
def getHNR(y, Fs, F0, Nfreqs):
print('holla')
NBins = len(y)
N0 = round(Fs / F0)
N0_delta = round(N0 * 0.1)
y = [x * z for x, z in zip(np.hamming(len(y)), y)]
fftY = np.fft(y, NBins)
aY = np.log10(abs(fftY))
ay = np.ifft(aY)
peakinx = np.zeros(np.floor(len(y)) / 2 / N0)
for k in range(1, len(peakinx)):
ayseg = ay[(k * N0 - N0_delta):(k * N0 + N0_delta)]
val, inx = max(
abs(ayseg)) # MAX does not behave the same - doesn't return inx??
peakinx[k] = inx + (k * N0) - N0_delta - 1
s_ayseg = np.sign(np.diff(ayseg))
l_inx = inx - np.find(
(np.sign(s_ayseg[inx - 1:-1:1]) != np.sign(inx)))[0] + 1
r_inx = inx + np.find(np.sign(s_ayseg[inx + 1:]) == np.sign(inx))[0]
l_inx = l_inx + k * N0 - N0_delta - 1
r_inx = r_inx + k * N0 - N0_delta - 1
for num in range(l_inx, r_inx):
ay[num] = 0
midL = round(len(y) / 2) + 1
ay[midL:] = ay[(midL - 1):-1:(midL - 1 - (len(ay) - midL))]
Nap = np.real(np.fft(ay))
N = Nap # ???? why?
Ha = aY - Nap # change these names ffs
Hdelta = F0 / Fs * len(y)
for f in [
num + 0.0001 for num in range(Hdelta, round(len(y) / 2), Hdelta)
]:
fstart = np.ceil(f - Hdelta)
Bdf = abs(min(Ha[fstart:round(f)]))
N[fstart:round(f)] = N[fstart:round(f)] - Bdf
H = aY - N
n = np.zeros(len(Nfreqs))
for k in range(1, len(Nfreqs)):
Ef = round(Nfreqs[k] / Fs * len(y))
n[k] = (20 * np.mean(H[1:Ef])) - (20 * np.mean(N[1:Ef]))
return n
def compute_predictions(self, test_x):
complex_array = self.post_mean_r + 1j * self.post_mean_i
print(self.w)
## symmetrize ##
real_pt = np.concatenate((self.post_mean_r, self.post_mean_r[1:]))/2.
im_pt = np.concatenate((self.post_mean_i, self.post_mean_i[1:]))/2.
plt.plot(real_pt)
plt.plot(im_pt)
plt.show()
cmplx_array = real_pt + 1j * im_pt
ft = np.ifft(cmplx_array)
plt.plot(ft)
def conv2d(smaller, larger):
"""convolve a pair of 2d numpy matrices
Uses fourier transform method, so faster if larger matrix
has dimensions of size 2**n
Actually right now the matrices must be the same size (will sort out
padding issues another day!)
"""
smallerFFT = numpy.fft2(smaller)
largerFFT = numpy.fft2(larger)
invFFT = numpy.ifft(smallerFFT*largerFFT)
return invFFT.real
def getHNR(y, Fs, F0, Nfreqs):
print 'holla'
NBins = len(y)
N0 = round(Fs/F0)
N0_delta = round(N0 * 0.1)
y = [x*z for x,z in zip(np.hamming(len(y)),y)]
fftY = np.fft(y, NBins)
aY = np.log10(abs(fftY))
ay = np.ifft(aY)
peakinx = np.zeros(np.floor(len(y))/2/N0)
for k in range(1, len(peakinx)):
ayseg = ay[k*N0 - N0_delta : k*N0 + N0_delta]
val, inx = max(abs(ayseg)) #MAX does not behave the same - doesn't return inx??
peakinx[k] = inx + (k * N0) - N0_delta - 1
s_ayseg = np.sign(np.diff(ayseg))
l_inx = inx - np.find((np.sign(s_ayseg[inx-1:-1:1]) != np.sign(inx)))[0] + 1
r_inx = inx + np.find(np.sign(s_ayseg[inx+1:]) == np.sign(inx))[0]
l_inx = l_inx + k*N0 - N0_delta - 1
r_inx = r_inx + k*N0 - N0_delta - 1
for num in range(l_inx, r_inx):
ay[num] = 0
midL = round(len(y)/2)+1
ay[midL:] = ay[midL-1: -1 : midL-1-(len(ay)-midL)]
Nap = np.real(np.fft(ay))
N = Nap #???? why?
Ha = aY - Nap #change these names ffs
Hdelta = F0/Fs * len(y)
for f in [num+0.0001 for num in range(Hdelta, round(len(y)/2), Hdelta)]:
fstart = np.ceil(f - Hdelta)
Bdf = abs(min(Ha[fstart:round(f)]))
N[fstart:round(f)] = N[fstart:round(f)] - Bdf
H = aY - N
n = np.zeros(len(Nfreqs))
for k in range(1, len(Nfreqs)):
Ef = round(Nfreqs[k] / Fs * len(y))
n[k] = (20 * np.mean(H[1:Ef])) - (20 * np.mean(N[1:Ef]))
return n
def findPulse(rgb):
N = int(rgb.size / 3)
k = 128
B = np.matrix('6,24')
P = np.zeros([1,N])
for n in range (1,N-1):
C = rgb[:,n:n+k-1]
Cprim = countC(C)
F = np.fft(Cprim, [], 2)
SS = np.matrix('0,1,-1;-2,1,1')
S = SS*F
Z = S[1,:] + np.absolute(S[1,:])/np.absolute(S[2,:])*S[2,:]
Zprim = Z *(np.absolute(Z)/np.absolute(np.sum(F,1)))
Zprim[:,1:B[1]-1] = 0
Zprim[:,B[2]+1::] = 0
Pprim = np.real(np.ifft(Zprim,[],2))
P[1,n:n+k-1] = P[k,n:n+k-1] + (Pprim - np.mean(Pprim))/np.std(Pprim)
return P
def idst(v,axis=-1):
n = len(v.shape)
N = v.shape[axis]
slices = [None]*3
for k in range(3):
slices[k] = []
for j in range(n):
slices[k].append(slice(None))
newshape = list(v.shape)
newshape[axis] = 2*(N+1)
Xt = np.zeros(newshape,np.complex128)
slices[0][axis] = slice(1,N+1)
slices[1][axis] = slice(N+2,None)
slices[2][axis] = slice(None,None,-1)
val = 2j*v
for k in range(3):
slices[k] = tuple(slices[k])
Xt[slices[0]] = -val
Xt[slices[1]] = val[slices[2]]
xhat = np.real(np.ifft(Xt,axis=axis))
return xhat[slices[0]]
def idst(v,axis=-1):
n = len(v.shape)
N = v.shape[axis]
slices = [None]*3
for k in range(3):
slices[k] = []
for j in range(n):
slices[k].append(slice(None))
newshape = list(v.shape)
newshape[axis] = 2*(N+1)
Xt = np.zeros(newshape,np.complex128)
slices[0][axis] = slice(1,N+1)
slices[1][axis] = slice(N+2,None)
slices[2][axis] = slice(None,None,-1)
val = 2j*v
for k in range(3):
slices[k] = tuple(slices[k])
Xt[slices[0]] = -val
Xt[slices[1]] = val[slices[2]]
xhat = np.real(np.ifft(Xt,axis=axis))
return xhat[slices[0]]
def find_peak_phi(self, cross_corr=False, img=None):
"""
RMClean.find_peak_phi(cross_corr=False, img=None)
Finds the index of the phi value at the peak of the residual image (or
the image passed to the function). The peak can be found by a simple
search algorithm, or by first cross correlating the image with the
RMSF.
Inputs:
cross_corr- Perform a cross correlation between RMSF and res. map
prior to seeking for the peak ala Heald 09
img- Image to search through. If none is given, the current
residual image will be used.
Outputs:
1- The pixel index of the phi value at the map peak
"""
phi_ndx = -1
peak_res = 0.
if img is None:
img = self.residual_map
if not cross_corr:
for i in range(len(img)):
if (abs(img[i]) > peak_res):
phi_ndx = i
peak_res = abs(img[i])
else:
temp_map_fft = numpy.fft(img)
temp_map = numpy.ifft(temp_map_fft.conjugate() *
numpy.fft(self.synth.rmsf))
phi_ndx = self.find_peak_phi(img=temp_map)
return phi_ndx
def dispersion(signal, beta, length, dt):
fs = np.fftfreq(len(signal), d=dt)
os = multiply(2 * np.pi, fs)
mulvec = np.array(multiply(-beta/2 * 1j * length, np.power(os, 2)))
return np.ifft(multiply(mulvec, np.fft(signal)))
def cor(x, y): # will change f and g back to x and y so things make sense
xft = np.fft(x)
yft = np.fft(y)
conyft = np.conj(yft)
return np.real(np.ifft(xft * conyft))
def computeIRs(self, *args, **kwdargs):
'''
Returns the scene response convolved by the hrtfs.
depends on the form of the HRTFs.
Computes the IRs from the scene given as a first argument, and convolves it correctly with the Receiver.
Sample usage:
receiver.computeIRs(scene,
'''
if len(args) == 1 and isinstance(args[0], Beam):
beam = args[0]
else:
scene = args[0]
args = args[1:]
beam = scene.render(self)
beam = beam[beam.get_reachedsource_index()]
newargs = [None]*(len(args)+1)
newargs[1:] = args
newargs[0] = beam
HRIRs = self.computeHRIRs(beam)
log_debug('HRIRs are of length (%i)' % (HRIRs.shape[0]))
kwdargs['binaural'] = False
kwdargs['collapse'] = False
IRs = scene.computeIRs(*newargs, **kwdargs)
# if isinstance(scene, SimpleScene):
# kwdargs['binaural'] = False
# else:
IRs = np.tile(np.asarray(IRs), (1, 2))
print IRs.shape
log_debug('Scene IRs are of length (%i)' % (IRs.shape[0]))
log_debug('Convoluting '+str(beam.nrays)+' scene responses with HRIRs')
ir_offset0 = np.min(np.argmin(1.0*(np.abs(IRs) < 1e-10), axis = 0))
ir_offset1 = IRs.shape[0]-np.min(np.argmin(1.0*(np.abs(IRs[::-1,:]) < 1e-10), axis = 0)) + 1
if ir_offset0 == ir_offset1 - 2:
log_debug('Environment impulse response is just one delay + gain')
# simple case, with only a delay and possibly a gain, so we just multiply
gains = np.tile(IRs[ir_offset0, :].reshape(1, IRs.shape[1]), (HRIRs.shape[0], 1))
convolution = HRIRs * gains
else:
# we do a real linear convolution, mostly because lengths never match
# it is costly so we try and trim the scene IRs that are quite often sparse
nir = ir_offset1 - ir_offset0
N = nir + HRIRs.shape[0] - 1
IRs_padded = np.vstack((IRs[ir_offset0:ir_offset1, :],
np.zeros((N - nir, IRs.shape[1]))))
HRIRs_padded = np.vstack((HRIRs,
np.zeros((IRs_padded.shape[0] - HRIRs.shape[0], HRIRs.shape[1]))))
convolution = np.zeros(HRIRs_padded.shape, dtype = complex)
convolution = np.ifft(np.fft.fft(IRs_padded, axis = 0)*np.fft.fft(HRIRs_padded, axis = 0), axis = 0).real
res = np.vstack((np.zeros((max(ir_offset0-1,0), 2*beam.nrays)), convolution))
log_debug('Collapsing final responses')
if scene.nsources > 1:
# More than one source
# TODO
allhrirs = zerosIR((res.shape[0], 2*scene.nsources), binaural = True)
relativecoordinates = []
target_source = np.unique(HRIRs.target_source)
for i in range(scene.nsources):
relativecoordinates.append(scene.sources[i].getRelativeSphericalCoords(
self, unit = 'deg'))
allhrirs[:, i] = np.sum(res[:, i*beamspersource:(i+1)*beamspersource], axis = 1)/float(beamspersource)#left
allhrirs[:, i+scene.nsources] = np.sum(res[:, beam.nrays+i*beamspersource:beam.nrays+(i+1)*beamspersource], axis = 1)/float(beamspersource)#right
if np.isnan(allhrirs).any():
log_debug('Output of getIRs will containt nans')
allhrirs.target_source = target_source
allhrirs.coordinates = relativecoordinates
return allhrirs
else:
# exactly one source
left = np.sum(res[:,:2], axis = 1)/beam.nrays
right = np.sum(res[:,2:], axis = 1)/beam.nrays
data = np.hstack((
left.reshape((len(left),1)), right.reshape((len(right), 1))
))
coordinates = scene.sources[0].getRelativeSphericalCoords(self)
return ImpulseResponse(data,
binaural = True,
samplerate = HRIRs.samplerate,
target_source = scene.sources[0].get_id(), coordinates = coordinates[1:])
def cmtm(x, y, dt=1.0, NW=8, qbias=0.0, confn=0.0, qplot=True):
"""
s, c, ph, ci, phi = cmtm(x,y,dt,NW,qbias,confn,qplot)
Multi-taper method coherence using adaptive weighting and correcting
for the bias inherent to coherence estimates. The 95% coherence
confidence level is computed by cohconf.py. In addition, a
Monte Carlo estimation procedure is available to estimate phase 95%
confidence limits.
Args:
x - Input data vector 1.
y - Input data vector 2.
dt - Sampling interval (default 8)
NW - Number of windows to use (default 8)
qbias - Correct coherence estimate for bias (default 0).
confn - Number of iterations to use in estimating phase
uncertainty using a Monte Carlo method. (default 0)
qplot - Plot the results. The upper tickmarks indicate the
bandwidth of the coherence and phase estimates.
Returns:
s - frequency
c - coherence
ph - phase
ci - 95% coherence confidence level
phi - 95% phase confidence interval, bias corrected
(add and subtract phi from ph).
required: cohconf.py, cohbias.py, cohbias.nc, scipy signal processing.
"""
# Local Variables: ci, fx, cb, qplot, Pk, E, qbias, vari, ys, phut, Fx, Fy,
# phl, ds, fkx, fky, tol, Ptemp, ph, phlt, pl, NW, phi, P1, pls, xs, i1,fy,
# wk, N, P, V, dt, confn, phu, a, c, b, Cxy, Pkx, Pky, iter, col, s, w, v,
# y, x, h, k
# Function calls: disp, cmtm, dpss, cohconf, conv, fill, fft, set, conj,
# repmat, find, size, plot, angle, figure, cohbias, min, axis, sum, si,
# sqrt, abs, zeros, rem, xlabel, pi, ciph, real, max, ylabel, sort,
# nargin, ones, randn, subplot, ifft, clf, gcf, fliplr, length, num2str,
# title, round, mean
# pre-checks
if NW < 1.5:
raise ValueError("Warning: NW must be greater or equal to 1.5")
print('Number of windows: ', NW)
if qbias == 1.:
print('Bias correction: On')
else:
print('Bias correction: Off')
print('Confidence Itera.: ', confn)
if qplot == 1.:
print('Plotting: On')
else:
print('Plotting: Off')
x = x.flatten(1)-np.mean(x)
y = y.flatten(1)-np.mean(y)
if x.shape[0] != y.shape[0]:
raise ValueError('Warning: the lengths of x and y must be equal.')
# define some parameters
N = x.shape[0]
k = np.max(np.round((2.*NW)), N)
k = np.max((k-1.), 1.)
s = np.arange(0., (1./dt-1./np.dot(N, dt)) +
(1./np.dot(N, dt)), 1./np.dot(N, dt)).conj().T
pls = np.arange(2., ((N+1.)/2.+1.)+1)
v = 2*NW-1 # approximate degrees of freedom
if y.shape % 2 == 1:
pls = pls[0:0-1.]
# Compute the discrete prolate spheroidal sequences,
# requires the spectral analysis toolbox.
[E, V] = dpss(N, NW, k)
# Compute the windowed DFTs.
fkx = np.fft((E[:, 0:k]*x[:, int(np.ones(1., k))-1]), N)
fky = np.fft((E[:, 0:k]*y[:, int(np.ones(1., k))-1]), N)
Pkx = np.abs(fkx)**2.
Pky = np.abs(fky)**2.
# Iteration to determine adaptive weights:
for i1 in np.arange(1, 3):
if i1 == 1:
vari = np.dot(x.conj().T, x)/N
Pk = Pkx
if i1 == 2:
vari = np.dot(y.conj().T, y)/N
Pk = Pky
P = (Pk[:, 0]+Pk[:, 1])/2.
# initial spectrum estimate
Ptemp = np.zeros((N, 1.))
P1 = np.zeros((N, 1.))
tol = np.dot(.0005, vari)/N
# usually within tolerance in about three iterations,
# see equations from [2] (P&W pp 368-370).
a = np.dot(vari, 1.-V)
while np.sum(np.abs((P-P1))/N) > tol:
b = np.dot(P, np.ones(1., k))/(np.dot(P, V.conj().T) +
np.dot(np.ones(N, 1.), a.conj().T))
# weights
wk = b**2.*np.dot(np.ones(N, 1.), V.conj().T)
# new spectral estimate
P1 = (np.sum((wk.conj().T*Pk.conj().T))/
np.sum(wk.conj().T)).conj().T
Ptemp = P1
P1 = P
P = Ptemp
# swap P and P1
if i1 == 1:
dotp1 = np.dot(np.sqrt(k), np.sqrt(wk))
fkxtmp = np.sum(np.sqrt(wk.conj().T)).conj().T
# fkx = dotp1*fkx/matcompat.repmat(fkxtmp, 1., k)
fkx = dotp1*fkx/np.kron(np.ones((1, k)), fkxtmp)
Fx = P
# Power density spectral estimate of x
if i1 == 2:
dotp1 = np.dot(np.sqrt(k), np.sqrt(wk))
fkytmp = np.sum(np.sqrt(wk.conj().T)).conj().T
# fky = dotp1*fky/matcompat.repmat(fkytmp, 1., k)
fky = dotp1*fky/np.kron(np.ones((1, k)), fkytmp)
Fy = P
# Power density spectral estimate of y
# As a check, the quantity sum(abs(fkx(pls,:))'.^2) is the same as Fx and
# the spectral estimate from pmtmPH.
# Compute coherence
Cxy = np.sum(np.array(np.hstack((fkx*np.conj(fky)))).conj().T)
ph = np.divide(np.angle(Cxy)*180., np.pi)
c = np.abs(Cxy)/np.sqrt((np.sum((np.abs(fkx.conj().T)**2.)) *
np.sum((np.abs(fky.conj().T)**2.))))
# correct for the bias of the estimate
if qbias == 1:
c = cohbias(v, c).conj().T
# Phase uncertainty estimates via Monte Carlo analysis.
if confn > 1:
cb = cohbias(v, c).conj().T
nlist = np.arange(1., (confn)+1)
ciph = np.zeros((nlist, x.shape[0])) # not sure about the cmtm return length
phi = np.zeros((nlist, x.shape[0])) # not sure about the cmtm return length
for iter in nlist:
if plt.rem(iter, 10.) == 0.:
print('phase confidence iteration: ', iter)
fx = np.fft(np.randn(x.shape)+1.)
fx = np.divide(fx, np.sum(np.abs(fx)))
fy = np.fft(np.randn(y.shape)+1.)
fy = np.divide(fy, np.sum(np.abs(fy)))
ys = np.real(np.ifft((fy*np.sqrt((1.-cb.conj().T**2.)))))
ys = ys+np.real(np.ifft((fx*cb.conj().T)))
xs = np.real(np.ifft(fx))
si, ciph[iter, :], phi[iter, :] = cmtm(xs, ys, dt, NW)
pl = np.round(np.dot(.975, iter))
# sorting and averaging to determine confidence levels.
phi = np.sort(phi)
phi = np.array(np.vstack((np.hstack((phi[int(pl)-1, :])), np.hstack((-phi[int((iter-pl+1.))-1, :])))))
phi = np.mean(phi)
phi = plt.conv(phi[0:], (np.array(np.hstack((1., 1., 1.)))/3.))
phi = phi[1:0-1.]
else:
phi = np.zeros(pls.shape[0])
# Cut to one-sided funtions
c = c[int(pls)-1]
s = s[int(pls)-1].conj().T
ph = ph[int(pls)-1]
# Coherence confidence level
ci = cohconf(v, .95)
# not corrected for bias, this is conservative.
ci = np.dot(ci, np.ones((c.shape[0])))
# plotting
if qplot:
phl = ph-phi
phu = ph+phi
# coherence
print('coherence plot')
# phase
print('phase plot')
return s, c, ph, ci, phi
def noise(signal, SNR):
return np.real(np.ifft(SNR / (SNR + 1) * np.fft(signal[:])))
Frames)) # Rayleigh variance = 1
fading_coeffs = np.fft(impulse_response)
else:
fading_coeffs = np.ones(NFFT, Frames)
# % DFT
TxNFFT = np.zeros(NFFT, Frames)
TxDFT = (1 / np.sqrt(N)) * np.fft(symbols)
# % Interleaving
# TxDFTInterleaved = Interleaving(TxDFT,g); % interleaving
TxDFTInterleaved = TxDFT # no intelreaving
# % Subcarrier mapping (Access mode)
TxNFFT[1:N, 1:Frames] = TxDFTInterleaved # Localized-FDMA
# TxNFFT(1:NFFT/N:NFFT,:) = TxDFT; % interleaved-FDMA
# % IFFT
Tx = (NFFT / sqrt(K)) * np.ifft(TxNFFT) # (sqrt(NFFT))*
# % CP and Channel
TxCP = np.mcat([Tx[np.mslice[- CP + 1:-1], np.mslice[:]], np.OMPCSEMI, Tx]) # cyclic prefix
for fr in np.mslice[1:Frames]:
TxCPChannel[:, fr] = filter[impulse_response[:, fr], 1, TxCP(np.mslice[:], fr)]
# end
# % GENERATE AND ADD AWGN
P_signal = np.mean(np.mean(abs(TxCPChannel) ** np.elpow ** 2))
P_noise = P_signal * 10 ** (-SNR_BER_db(j) / 10)
noise_norm = sqrt(0.5) * complex(randn(NFFT + CP, Frames), randn(NFFT + CP, Frames))
En = sqrt(P_noise) * noise_norm
TxCPChannelNoise = TxCPChannel + En
# % Remove CP
TxChannelNoise = TxCPChannelNoise(np.mslice[CP + 1:end], np.mslice[:])
# % Channel Equalization
mmse = np.conj(fading_coeffs) / np.eldiv / ((abs(fading_coeffs) ** np.elpow ** 2) + (P_noise / P_signal))
def ft(self,axes,tolerance = 1e-5,cosine=False,verbose = False,unitary=None,**kwargs):
r"""This performs a Fourier transform along the axes identified by the string or list of strings `axes`.
It adjusts normalization and units so that the result conforms to
:math:`\tilde{s}(f)=\int_{x_{min}}^{x_{max}} s(t) e^{-i 2 \pi f t} dt`
**pre-FT**, we use the axis to cyclically permute :math:`t=0` to the first index
**post-FT**, we assume that the data has previously been IFT'd
If this is the case, passing ``shift=True`` will cause an error
If this is not the case, passing ``shift=True`` generates a standard fftshift
``shift=None`` will choose True, if and only if this is not the case
Parameters
----------
pad : int or boolean
`pad` specifies a zero-filling. If it's a number, then it gives
the length of the zero-filled dimension. If it is just `True`,
then the size of the dimension is determined by rounding the
dimension size up to the nearest integral power of 2.
automix : double
`automix` can be set to the approximate frequency value. This is
useful for the specific case where the data has been captured on a
sampling scope, and it's severely aliased over.
cosine : boolean
yields a sum of the fft and ifft, for a cosine transform
unitary : boolean (None)
return a result that is vector-unitary
"""
if self.data.dtype == np.float64:
self.data = np.complex128(self.data) # everything is done assuming complex data
#{{{ process arguments
axes = self._possibly_one_axis(axes)
if (isinstance(axes, str)):
axes = [axes]
#{{{ check and set the FT property
for j in axes:
if j not in self.dimlabels: raise ValueError("the axis "+j+" doesn't exist")
if self.get_ft_prop(j):
errmsg = "This data has been FT'd along "+str(j)
raise ValueError(errmsg + "-- you can't FT"
" again unless you explicitly"
" .set_prop('FT',None), which is"
" probably not what you want to do")
self.set_ft_prop(j) # sets the "FT" property to "true"
#}}}
if 'shiftornot' in kwargs:
raise ValueError("shiftornot is obsolete --> use shift instead")
shift,pad,automix = process_kwargs([
('shift',False),
('pad',False),
('automix',False),
],
kwargs)
if not (isinstance(shift, list)):
shift = [shift]*len(axes)
if not (isinstance(unitary, list)):
unitary = [unitary]*len(axes)
for j in range(0,len(axes)):
#print("called FT on",axes[j],", unitary",unitary[j],"and property",
# self.get_ft_prop(axes[j],"unitary"))
if self.get_ft_prop(axes[j],"unitary") is None: # has not been called
if unitary[j] is None:
unitary[j]=False
self.set_ft_prop(axes[j],"unitary",unitary[j])
else:
if unitary[j] is None:
unitary[j] = self.get_ft_prop(axes[j],"unitary")
else:
raise ValueError("Call ft or ift with unitary only the first time, and it will be set thereafter.\nOR if you really want to override mid-way use self.set_ft_prop(axisname,\"unitary\",True/False) before calling ft or ift")
#print("for",axes[j],"set to",unitary[j])
#}}}
for j in range(0,len(axes)):
do_post_shift = False
p2_post_discrepancy = None
p2_pre_discrepancy = None
#{{{ if this is NOT the source data, I need to mark it as not alias-safe!
if self.get_ft_prop(axes[j],['start','freq']) is None:# this is the same
# as saying that I have NOT run .ift() on this data yet,
# meaning that I must have started with time as the
# source data, and am now constructing an artificial and
# possibly aliased frequency-domain
if self.get_ft_prop(axes[j],['freq','not','aliased']) is not True:#
# has been manually set/overridden
self.set_ft_prop(axes[j],['freq','not','aliased'],False)
#{{{ but on the other hand, I am taking the time as the
# not-aliased "source", so as long as I haven't explicitly set it as
# unsafe, declare it "safe"
if self.get_ft_prop(axes[j],['time','not','aliased']) is not False:
self.set_ft_prop(axes[j],['time','not','aliased'])
#}}}
#}}}
#{{{ grab the axes, set the units, and determine padded_length
if self.get_units(axes[j]) is not None:
self.set_units(axes[j],self._ft_conj(self.get_units(axes[j])))
try:
thisaxis = self.dimlabels.index(axes[j])
except:
raise RuntimeError(strm("I can't find",axes[j],
"dimlabels is: ",self.dimlabels))
padded_length = self.data.shape[thisaxis]
if pad is True:
padded_length = int(2**(np.ceil(np.log2(padded_length))))
elif pad:
padded_length = pad
u = self.getaxis(axes[j]) # here, u is time
if u is None:
raise ValueError("seems to be no axis for"+repr(axes[j])+"set an axis before you try to FT")
#}}}
self.set_ft_prop(axes[j],['start','time'],u[0]) # before anything else, store the start time
#{{{ calculate new axis and post-IFT shift..
# Calculate it first, in case it's non-integral. Also note that
# I calculate the post-discrepancy here
#{{{ need to calculate du and all checks here so I can calculate new u
du = check_ascending_axis(u,tolerance,"In order to perform FT or IFT")
self.set_ft_prop(axes[j],['dt'],du)
#}}}
dv = np.double(1) / du / np.double(padded_length) # so padded length gives the SW
self.set_ft_prop(axes[j],['df'],dv)
v = r_[0:padded_length] * dv # v is the name of the *new* axis. Note
# that we stop one index before the SW, which is what we want
desired_startpoint = self.get_ft_prop(axes[j],['start','freq'])
if desired_startpoint is not None:# FT_start_freq is set
if shift[j]:
raise ValueError("you are not allowed to shift an array for"
" which the index for $f=0$ has already been"
" determined!")
if verbose: print("check for p2_post_discrepancy")
if verbose: print("desired startpoint",desired_startpoint)
p2_post,p2_post_discrepancy,alias_shift_post = _find_index(v,origin = desired_startpoint,verbose = verbose)
if verbose: print("p2_post,p2_post_discrepancy,alias_shift_post,v at p2_post, and v at p2_post-1:", p2_post, p2_post_discrepancy, alias_shift_post, v[p2_post], v[p2_post - 1])
if p2_post != 0 or p2_post_discrepancy is not None:
do_post_shift = True
else:
do_post_shift = False
elif shift[j] or shift[j] is None: # a default fftshift
if automix:
raise ValueError("You can't use automix and shift at the same time --> it doesn't make sense")
n = padded_length
p2_post = (n+1) // 2 # this is the starting index of what starts out as the second half (// is floordiv) -- copied from scipy -- this essentially rounds up (by default assigning more negative frequencies than positive ones)
alias_shift_post = 0
do_post_shift = True
#{{{ if I start with an alias-safe axis, and perform a
# traditional shift, I get an alias-safe axis
if self.get_ft_prop(axes[j],'time_not_aliased'):
self.set_ft_prop(axes[j],'freq_not_aliased')
#}}}
#}}}
#{{{ I might need to perform a phase-shift now...
# in order to adjust for a final u-axis that doesn't pass
# exactly through zero
if p2_post_discrepancy is not None:
asrt_msg = r"""You are trying to shift the frequency axis by (%d+%g) du (%g).
In order to shift by a frequency that is not
integral w.r.t. the frequency resolution step, you need to be sure
that the time-domain spectrum is not aliased.
This is typically achieved by starting from a time domain spectrum and
generating the frequency domain by an FT.
If you **know** by other means that the time-domain spectrum
is not aliased, you can also set the `time_not_aliased` FT property
to `True`."""%(p2_post, p2_post_discrepancy, du)
assert self.get_ft_prop(axes[j],['time','not','aliased']),(asrt_msg)
assert abs(p2_post_discrepancy)<abs(dv),("I expect the discrepancy to be"
" smaller than dv ({:0.2f}), but it's {:0.2f} -- what's going"
" on??").format(dv,p2_post_discrepancy)
phaseshift = self.fromaxis(axes[j],
lambda q: np.exp(-1j*2*pi*q*p2_post_discrepancy))
try:
self.data *= phaseshift.data
except TypeError as e:
if self.data.dtype != 'complex128':
raise TypeError("You tried to ft nddata that was of type "+str(self.data.dtype))
else:
raise TypeError(e)
#}}}
#{{{ do zero-filling manually and first, so I can properly pre-shift the data
if not pad is False:
newdata = list(self.data.shape)
newdata[thisaxis] = padded_length
targetslice = [slice(None,None,None)] * len(newdata)
targetslice[thisaxis] = slice(None,self.data.shape[thisaxis])
targetslice = tuple(targetslice)
newdata = np.zeros(newdata,dtype = self.data.dtype)
newdata[targetslice] = self.data
self.data = newdata
u = r_[0:padded_length] * du + u[0]
#}}}
#{{{ pre-FT shift so that we start at u=0
p2_pre,p2_pre_discrepancy,alias_shift_pre = _find_index(u,verbose = verbose)
self._ft_shift(thisaxis,p2_pre)
#}}}
#{{{ the actual (I)FFT portion of the routine
if cosine:
self.data = np.fft.fft(self.data,
axis=thisaxis) + np.ifft(self.data,
axis=thisaxis)
self.data *= 0.5
else:
self.data = np.fft.fft(self.data,
axis=thisaxis)
self.axis_coords[thisaxis] = v
#}}}
#{{{ actually run the post-FT shift
if do_post_shift:
self._ft_shift(thisaxis,p2_post,shift_axis = True)
if alias_shift_post != 0:
self.axis_coords[thisaxis] += alias_shift_post
#}}}
#{{{ finally, I must allow for the possibility that "p2_post" in the
# pre-shift was not actually at zero, but at some other value, and I
# must apply a phase shift to reflect the fact that I need to add
# back that time
if p2_post_discrepancy is not None:
if verbose: print("adjusting axis by",p2_post_discrepancy,"where du is",u[1]-u[0])
self.axis_coords[thisaxis][:] += p2_post_discrepancy # reflect the
# p2_post_discrepancy that we have already incorporated via a
# phase-shift above
#}}}
#{{{ adjust the normalization appropriately
if unitary[j]:
self.data /= np.sqrt(padded_length)
else:
self.data *= du # this gives the units in the integral noted in the docstring
#}}}
#{{{ finally, if "p2_pre" for the pre-shift didn't correspond exactly to
# zero, then the pre-ft data was shifted, and I must reflect
# that by performing a post-ft phase shift
if p2_pre_discrepancy is not None:
assert abs(p2_pre_discrepancy)<abs(du) or np.isclose(
abs(p2_pre_discrepancy),abs(du)),("I expect the discrepancy to be"
" smaller than du ({:0.5g}), but it's {:0.5g} -- what's going"
" on??").format(du,p2_pre_discrepancy)
result = self * self.fromaxis(axes[j],
lambda f: np.exp(1j*2*pi*f*p2_pre_discrepancy))
self.data = result.data
#}}}
if automix:
sw = 1.0/du
carrier = abs(self).mean_all_but(axes[j]).argmax(axes[j]).data
if verbose: print("I find carrier at",carrier)
add_to_axis = (automix - carrier) / sw
if verbose: print("which is",add_to_axis,"times the sw of",sw,"off from the automix value of",automix)
x = self.getaxis(axes[j])
x += np.round(add_to_axis)*sw
return self
"""
import numpy as np
data_filename = 'data.txt'
time_data = []
freq_data = []
data_file = open(data_filename, 'r')
error_file = open('error_for_' + data_filename, 'w+')
for line in data_file:
line = line.split(';')
time_data.append(list(line[0]))
freq_data.append(list(line[1]))
num_entries = len(time_data)
num_values = len(time_data[0])
for i in range(num_entries):
freq_data_check = np.real(np.fft(time_data[i]))
time_data_check = np.real(np.ifft(freq_data[i]))
for j in range(num_values):
error_file.write(str(freq_data[i][j] - freq_data_check[j]))
error_file.write(' ')
error_file.write(' ')
for j in range(num_values):
error_file.write(str(time_data[i][j] - time_data_check[j]))
error_file.write(' ')
error_file.write('\n')
data_file.close()
error_file.close()
def correlation(x, h):
'''This function calculates the correlation function between the data(x)
and a normalized template(h).'''
func = numpy.fft(x) * numpy.conjugate(numpy.fft(h))
return numpy.ifft(func)
def cor(f, g):
xft = np.fft(f)
yft = np.fft(g)
conyft = np.conj(yft)
return np.real(np.ifft(xft * conyft))
def smoothGaussian(array,sigma):
return numpy.ifft(numpy.fft(array)*1/numpy.sqrt(2*numpy.pi)/sigma*numpy.exp(numpy.arange(0,len(array),1.0)**2/2.0/sigma**2))