def test_depth_kwarg(self):
nz = 100
zN2 = 0.5*nz**-1 + np.arange(nz, dtype=np.float64)/nz
zU = 0.5*nz**-1 + np.arange(nz+1, dtype=np.float64)/nz
N2 = np.full(nz, 1.)
f0 = 1.
#beta = 1e-6
beta = 0.
Nx = 1
Ny = 1
dx = .1
dy = .1
k = fft.fftshift( fft.fftfreq(Nx, dx) )
l = fft.fftshift( fft.fftfreq(Ny, dy) )
ubar = np.zeros(nz+1)
vbar = np.zeros(nz+1)
etax = np.zeros(2)
etay = np.zeros(2)
with self.assertRaises(ValueError):
z, growth_rate, vertical_modes = modes.instability_analysis_from_N2_profile(
zN2, N2, f0, beta, k, l, zU, ubar, vbar, etax, etay, depth=zN2[-5]
)
# no error expected
z, growth_rate, vertical_mode = modes.instability_analysis_from_N2_profile(
zN2, N2, f0, beta, k, l, zU, ubar, vbar, etax, etay, depth=1.1
)
def analyze_audio(prefix):
output = []
rate, data = wavfile.read('%s.wav' % prefix)
dt = 1./rate
T = dt * data.shape[0]
output.append('%s %s' % (dt, T))
tvec = np.arange(0, T, dt)
sig0 = data[:, 0]
sig1 = data[:, 1]
output.append('%s %s' % (np.sum(sig0), np.sum(sig1)))
plt.clf()
plt.plot(tvec, sig0)
plt.plot(tvec, sig1)
xtickarray = range(0, 12, 2)
plt.xticks(xtickarray, ['%d s' % x for x in xtickarray])
plt.savefig('%s_time.png' % prefix)
plt.clf()
samp_freq0 = fftpack.fftfreq(sig0.size, d=dt)
sig_fft0 = fftpack.fft(sig0)
samp_freq1 = fftpack.fftfreq(sig1.size, d=dt)
sig_fft1 = fftpack.fft(sig1)
plt.plot(np.log(np.abs(samp_freq0)+1e-9), np.abs(sig_fft0))
plt.plot(np.log(np.abs(samp_freq1)+1e-9), np.abs(sig_fft1))
plt.xlim(np.log(10), np.log(40e3))
xtickarray = np.log(np.array([20, 1e2, 3e2, 1e3, 3e3, 10e3, 30e3]))
plt.xticks(xtickarray, ['20Hz', '100Hz', '300Hz', '1kHz', '3kHz', '10kHz',
'30kHz'])
plt.savefig('%s_freq.png' % prefix)
return '\n'.join(output)
def genwavenumber(nlon):
if (nlon%2 == 0):
wavenumber = fftpack.fftshift(fftpack.fftfreq(nlon)*nlon)[1:]
else:
wavenumber = fftpack.fftshift(fftpack.fftfreq(nlon)*nlon)
return wavenumber
def make_audio_analysis_plots(infile, prefix='temp', make_plots=True,
do_fft=True, fft_sum=None):
''' create frequency plot '''
import numpy as np
from scipy import fftpack
from scipy.io import wavfile
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as pl
if not os.path.exists(infile):
return -1
try:
rate, data = wavfile.read(infile)
except ValueError:
print('error reading wav file')
return -1
dt_ = 1./rate
time_ = dt_ * data.shape[0]
tvec = np.arange(0, time_, dt_)
sig0 = data[:, 0]
sig1 = data[:, 1]
if not tvec.shape == sig0.shape == sig1.shape:
return -1
if not do_fft:
fft_sum_ = float(np.sum(np.abs(sig0)))
if hasattr(fft_sum, 'value'):
fft_sum.value = fft_sum_
return fft_sum_
if make_plots:
pl.clf()
pl.plot(tvec, sig0)
pl.plot(tvec, sig1)
xtickarray = range(0, 12, 2)
pl.xticks(xtickarray, ['%d s' % x for x in xtickarray])
pl.savefig('%s/%s_time.png' % (HOMEDIR, prefix))
pl.clf()
samp_freq0 = fftpack.fftfreq(sig0.size, d=dt_)
sig_fft0 = fftpack.fft(sig0)
samp_freq1 = fftpack.fftfreq(sig1.size, d=dt_)
sig_fft1 = fftpack.fft(sig1)
if make_plots:
pl.clf()
pl.plot(np.log(np.abs(samp_freq0)+1e-9), np.abs(sig_fft0))
pl.plot(np.log(np.abs(samp_freq1)+1e-9), np.abs(sig_fft1))
pl.xlim(np.log(10), np.log(40e3))
xtickarray = np.log(np.array([20, 1e2, 3e2, 1e3, 3e3, 10e3, 30e3]))
pl.xticks(xtickarray, ['20Hz', '100Hz', '300Hz', '1kHz', '3kHz',
'10kHz', '30kHz'])
pl.savefig('%s/%s_fft.png' % (HOMEDIR, prefix))
pl.clf()
run_command('mv %s/%s_time.png %s/%s_fft.png %s/public_html/videos/'
% (HOMEDIR, prefix, HOMEDIR, prefix, HOMEDIR))
fft_sum_ = float(np.sum(np.abs(sig_fft0)))
if hasattr(fft_sum, 'value'):
fft_sum.value = fft_sum_
return fft_sum_
def test_definition(self):
x = [0,1,2,3,4,-4,-3,-2,-1]
assert_array_almost_equal(9*fftfreq(9),x)
assert_array_almost_equal(9*pi*fftfreq(9,pi),x)
x = [0,1,2,3,4,-5,-4,-3,-2,-1]
assert_array_almost_equal(10*fftfreq(10),x)
assert_array_almost_equal(10*pi*fftfreq(10,pi),x)
def invert_vort(uc, dx=dx, dy=dy, nx=nx, ny=ny, geom=tad.geom):
ucv = geom.validview(uc)
vort = ucv[0]
u = ucv[1]
v = ucv[2]
f = fft2(vort)
nx, ny = vort.shape
scal_y = 2*pi/dy/ny
scal_x = 2*pi/dx/nx
k = fftfreq(nx, 1/nx)[:,None] * 1j * scal_x
l = fftfreq(ny, 1/ny)[None,:] * 1j * scal_y
lapl = k**2 + l**2
lapl[0,0] = 1.0
psi = f/lapl
u[:] = -real(ifft2(psi * l))
v[:] = real(ifft2(psi * k))
return uc
def deflection_calculation(x, y, topo, rho_t, rho_c, rho_m, Te, E, nu, padding=0):
"""
Calculates the deflection due to a topographic load for a plate of constant
thickness Te.
Uses the equation:
F[w] = rho_t/(rho_m-rho_c) phi_e(k) F[topo]
"""
ny, nx = np.shape(topo)
dx = abs(x[0][1] - x[0][0])
dy = abs(y[1][0] - y[0][0])
if padding != 0:
ny_pad, nx_pad = ny*padding, nx*padding
topo = np.pad(topo, (ny_pad,nx_pad), 'constant', constant_values=0)
else:
nx_pad, ny_pad = 0, 0
fx = fftpack.fftfreq(nx + 2*nx_pad, dx)
fy = fftpack.fftfreq(ny + 2*ny_pad, dy)
fx, fy = np.meshgrid(fx, fy)
k = 2*np.pi*np.sqrt(fx**2 + fy**2)
F_w = rho_t/(rho_m - rho_c)*phi_e(k, Te, rho_c, rho_m, E, nu)*fftpack.fft2(topo)
w = np.real(fftpack.ifft2(F_w))
if padding != 0:
w = w[ny_pad:-ny_pad, nx_pad:-nx_pad]
return w
def icwt2d(self, da=0.25):
'''
Inverse bi-dimensional continuous wavelet transform as in Wang and
Lu (2010), equation [5].
Parameters
----------
da : float, optional
Spacing in the frequency axis.
'''
if self.Wf is None:
raise TypeError("Run cwt2D before icwt2D")
m0, l0, k0 = self.Wf.shape
if m0 != self.scales.size:
raise Warning('Scale parameter array shape does not match\
wavelet transform array shape.')
# Calculates the zonal and meridional wave numters.
L, K = 2 ** int(np.ceil(np.log2(l0))), 2 ** int(np.ceil(np.log2(k0)))
# Calculates the zonal and meridional wave numbers.
l, k = fftfreq(L, self.dy), fftfreq(K, self.dx)
# Creates empty inverse wavelet transform array and fills it for every
# discrete scale using the convolution theorem.
self.iWf = np.zeros((m0, L, K), 'complex')
for i, an in enumerate(self.scales):
psi_ft_bar = an * self.wavelet.psi_ft(an * k, an * l)
W_ft = fftn(self.Wf[i, :, :], s=(L, K))
self.iWf[i, :, :] = ifftn(W_ft * psi_ft_bar, s=(L, K)) *\
da / an ** 2.
self.iWf = self.iWf[:, :l0, :k0].real.sum(axis=0) / self.wavelet.cpsi
return self
def direct_shift(x,a,period=None):
n = len(x)
if period is None:
k = fftfreq(n)*1j*n
else:
k = fftfreq(n)*2j*pi/period*n
return ifft(fft(x)*exp(k*a)).real
def __init__(self, x, y, s, detrend=True, window=False, **kwargs):
# r-space
self.x = np.asanyarray(x)
self.y = np.asanyarray(y)
self.s = np.asanyarray(s)
assert len(self.x.shape) == 2
assert self.x.shape == self.y.shape == self.s.shape
assert self.x.size == self.y.size == self.s.size
# r-space spacing
self.dx = self._delta(self.x, np.index_exp[0,0], np.index_exp[1,0])
self.dy = self._delta(self.y, np.index_exp[0,0], np.index_exp[0,1])
# r-space samples
self.n0 = self.x.shape[0]
self.n1 = self.x.shape[1]
# r-space lengths
self.lx = self.n0 * self.dx
self.ly = self.n1 * self.dy
# k-space
u = fftpack.fftshift(fftpack.fftfreq(self.n0))
v = fftpack.fftshift(fftpack.fftfreq(self.n1))
self.u, self.v = np.meshgrid(u, v, indexing='ij')
# k-space spacing
self.du = self._delta(self.u, np.index_exp[0,0], np.index_exp[1,0])
self.dv = self._delta(self.v, np.index_exp[0,0], np.index_exp[0,1])
# k-space lengths
self.lu = self.n0 * self.du
self.lv = self.n1 * self.dv
# nyquist
try:
self.nyquist_u = 0.5/self.dx
except ZeroDivisionError:
self.nyquist_u = 0.0
try:
self.nyquist_v = 0.5/self.dy
except ZeroDivisionError:
self.nyquist_v = 0.0
self.k = np.sqrt(self.u**2 + self.v**2)
# detrend the signal
if detrend:
self.s = signal.detrend(self.s)
# apply window to signal
if window:
self._window()
self.s = self.s * self.window
# compute the FFT
self.fft = fftpack.fftshift(fftpack.fft2(self.s))
self.power = self.fft.real**2 + self.fft.imag**2
def __init__(self, cube, header, phys_units=False):
super(VCS, self).__init__()
self.header = header
self.cube = cube
self.fftcube = None
self.correlated_cube = None
self.ps1D = None
self.phys_units = phys_units
if np.isnan(self.cube).any():
self.cube[np.isnan(self.cube)] = 0
# Feel like this should be more specific
self.good_channel_count = np.sum(self.cube[0, :, :] != 0)
else:
self.good_channel_count = float(
self.cube.shape[1] * self.cube.shape[2])
# Lazy check to make sure we have units of km/s
if np.abs(self.header["CDELT3"]) > 1:
self.vel_to_pix = np.abs(self.header["CDELT3"]) / 1000.
else:
self.vel_to_pix = np.abs(self.header["CDELT3"])
self.vel_channels = np.arange(1, self.cube.shape[0], 1)
if self.phys_units:
self.vel_freqs = np.abs(
fftfreq(self.cube.shape[0])) / self.vel_to_pix
else:
self.vel_freqs = np.abs(fftfreq(self.cube.shape[0]))
def mkgrad(self,data):
"""Calculate gradient by convolution with appropriate gaussian filter"""
n1=data.shape[0]
if(not self.n or n1 != self.n):
self.n= n1
self.grad_multiplyer= fftfreq(n1)*numpy.exp(-4*fftfreq(n1)**2)
data_f = fft(data)
grad_f = data_f*self.grad_multiplyer
return numpy.absolute(ifft(grad))
def get_mps(t, freq, spec):
"Computes the MPS of a spectrogram (idealy a log-spectrogram) or other REAL time-freq representation"
mps = fftshift(fft2(spec))
amps = np.real(mps * np.conj(mps))
nf = mps.shape[0]
nt = mps.shape[1]
wfreq = fftshift(fftfreq(nf, d=freq[1] - freq[0]))
wt = fftshift(fftfreq(nt, d=t[1] - t[0]))
return wt, wfreq, mps, amps
def makeImageFromSf(self, sfx, sf, reduceNoise=True):
"""Invert SF all the way back to ImageI."""
self.invertSf(sfx, sf)
self.invertAcovf1d(reduceNoise=reduceNoise)
self.invertAcovf2d(useI=True)
self.invertPsd2d(useI=True)
self.invertFft(useI=True)
self.xfreq = fftpack.fftfreq(self.nx, 1.0)
self.yfreq = fftpack.fftfreq(self.ny, 1.0)
return
def __init__(self, datain, spd, tim_taper=0.1):
"""Arguments:
'datain' -- the data to be filtered. dimension must be (time, lat, lon)
'spd' -- samples per day
'tim_taper' -- tapering ratio by cos. applay tapering first and last tim_taper%
samples. default is cos20 tapering
"""
ntim, nlat, nlon = datain.shape
#remove the lowest three harmonics of the seasonal cycle (WK99, WKW03)
## if ntim > 365*spd/3:
## rf = fftpack.rfft(datain,axis=0)
## freq = fftpack.rfftfreq(ntim*spd, d=1./float(spd))
## rf[(freq <= 3./365) & (freq >=1./365),:,:] = 0.0 #freq<=3./365 only??
## datain = fftpack.irfft(rf,axis=0)
#remove dominal trend
data = signal.detrend(datain, axis=0)
#tapering
if tim_taper == 'hann':
window = signal.hann(ntim)
data = data * window[:,NA,NA]
elif tim_taper > 0:
#taper by cos tapering same dtype as input array
tp = int(ntim*tim_taper)
window = numpy.ones(ntim, dtype=datain.dtype)
x = numpy.arange(tp)
window[:tp] = 0.5*(1.0-numpy.cos(x*pi/tp))
window[-tp:] = 0.5*(1.0-numpy.cos(x[::-1]*pi/tp))
data = data * window[:,NA,NA]
#FFT
self.fftdata = fftpack.fft2(data, axes=(0,2))
#Note
# fft is defined by exp(-ikx), so to adjust exp(ikx) multipried minus
wavenumber = -fftpack.fftfreq(nlon)*nlon
frequency = fftpack.fftfreq(ntim, d=1./float(spd))
knum, freq = numpy.meshgrid(wavenumber, frequency)
#make f<0 domain same as f>0 domain
#CAUTION: wave definition is exp(i(k*x-omega*t)) but FFT definition exp(-ikx)
#so cahnge sign
knum[freq<0] = -knum[freq<0]
freq = numpy.abs(freq)
self.knum = knum
self.freq = freq
self.wavenumber = wavenumber
self.frequency = frequency
def test_Eady(self, atol=5e-2, nz=20, Ah=0.):
""" Eady setup
"""
###########
# prepare parameters for Eady
###########
nz = nz
zin = np.arange(nz+1, dtype=np.float64)/nz
N2 = np.full(nz, 1.)
f0 = 1.
beta = 0.
Nx = 10
Ny = 1
dx = 1e-1
dy = 1e-1
k = fft.fftshift( fft.fftfreq(Nx, dx) )
l = fft.fftshift( fft.fftfreq(Ny, dy) )
vbar = np.zeros(nz+1)
ubar = zin
etax = np.zeros(2)
etay = np.zeros(2)
z, growth_rate, vertical_modes = \
modes.instability_analysis_from_N2_profile(
.5*(zin[1:]+zin[:-1]), N2, f0, beta, k, l,
zin, ubar, vbar, etax, etay, depth=1., sort='LI', num=2
)
self.assertEqual(nz+1, vertical_modes.shape[0],
msg='modes array must be in the right shape')
self.assertTrue(np.all( np.diff(
growth_rate.reshape((growth_rate.shape[0], len(k)*len(l))).imag.max(axis=1) ) <= 0.),
msg='imaginary part of modes should be descending')
mode_amplitude1 = (np.absolute(vertical_modes[:, 0])**2).sum(axis=0)
self.assertTrue(np.allclose(1., mode_amplitude1),
msg='mode1 should be normalized to amplitude of 1 at all horizontal wavenumber points')
mode_amplitude2 = (np.absolute(vertical_modes[:, 1])**2).sum(axis=0)
self.assertTrue(np.allclose(1., mode_amplitude2),
msg='mode2 should be normalized to amplitude of 1 at all horizontal wavenumber points')
#########
# Analytical solution for Eady growth rate
#########
growthEady = np.zeros(len(k))
for i in range(len(k)):
if (k[i]==0) or ((np.tanh(.5*k[i])**-1 - .5*k[i]) * (.5*k[i] - np.tanh(.5*k[i])) < 0):
growthEady[i] = 0.
else:
growthEady[i] = ubar.max() * np.sqrt( (np.tanh(.5*k[i])**-1 - .5*k[i]) * (.5*k[i] - np.tanh(.5*k[i])) )
self.assertTrue( np.allclose(growth_rate.imag[0, 0, :], growthEady, atol=atol),
msg='The numerical growth rates should be close to the analytical Eady solution' )
def mps(spectrogram, df, dt):
"""
Compute the modulation power spectrum for a given spectrogram.
"""
#normalize and mean center the spectrogram
sdata = copy.copy(spectrogram)
sdata /= sdata.max()
sdata -= sdata.mean()
#take the 2D FFT and center it
smps = fft2(sdata)
smps = fftshift(smps)
#compute the log amplitude
mps_logamp = 20*np.log10(np.abs(smps)**2)
mps_logamp[mps_logamp < 0.0] = 0.0
#compute the phase
mps_phase = np.angle(smps)
#compute the axes
nf = mps_logamp.shape[0]
nt = mps_logamp.shape[1]
spectral_freq = fftshift(fftfreq(nf, d=df))
temporal_freq = fftshift(fftfreq(nt, d=dt))
"""
nb = sdata.shape[1]
dwf = np.zeros(nb)
for ib in range(int(np.ceil((nb+1)/2.0))+1):
posindx = ib
negindx = nb-ib+2
print 'ib=%d, posindx=%d, negindx=%d' % (ib, posindx, negindx)
dwf[ib]= (ib-1)*(1.0/(df*nb))
if ib > 1:
dwf[negindx] =- dwf[ib]
nt = sdata.shape[0]
dwt = np.zeros(nt)
for it in range(0, int(np.ceil((nt+1)/2.0))+1):
posindx = it
negindx = nt-it+2
print 'it=%d, posindx=%d, negindx=%d' % (it, posindx, negindx)
dwt[it] = (it-1)*(1.0/(nt*dt))
if it > 1 :
dwt[negindx] = -dwt[it]
spectral_freq = dwf
temporal_freq = dwt
"""
return temporal_freq,spectral_freq,mps_logamp,mps_phase
def __init__(self,shape,lengths):
self.lengths=lengths
self.shape=shape
self.Inv_Laplacian=(np.dstack(np.meshgrid(fftpack.fftfreq(self.shape[1],1.0/self.shape[1]),
fftpack.fftfreq(self.shape[0],1.0/self.shape[0])))**2).sum(-1)
self.Inv_Laplacian[self.Inv_Laplacian<1.0]=1.0
self.Inv_Laplacian=1.0
self.Inv_Laplacian/=self.lengths.area_lat_lon
#Define the vector calculus in spherical harmonics:
self.spharm=horizontal_vector_calculus_spherical_harmonics(self.shape,self.lengths)
return
def solve_sqg(self):
import scipy.fftpack as fft
import numpy as np
from math import pi
self.precondition()
dx = self.dx
dy = self.dy
rhos = self.ssd
bhat = fft.fft2( - 9.81 * rhos / self.rho0) # calculate bouyance
ny, nx = rhos.shape
nz = self.nz
k = 2 * pi * fft.fftfreq(nx)
l = 2 * pi * fft.fftfreq(ny)
ipsihat = np.zeros((nz+3, ny, nx))*complex(0, 0)
Q = np.zeros((nz + 1, 1), dtype='float64'); Q[[0,-1]] = 0.0 # for interior PV, no used in this version
# cutoff value
ck, cl = 2 * pi / self.filterL, 2 * pi / self.filterL
# loop through wavenumbers
bhats = np.zeros_like(bhat)
for ik in np.arange(k.size):
for il in np.arange(l.size):
wv2 = ((k[ik] / dx[il, 0]) ** 2 + (l[il] / dy[0, ik]) ** 2)
if wv2 > (ck * ck + cl * cl):
bhats[il,ik] = bhat[il,ik]
right = - bhat[il, ik] / self.f0 * self.Rp
left = self.M - wv2 * np.eye(self.nz+1)
ipsihat[1:-1, il, ik] = np.linalg.solve(left, right).flatten()
else:
print 'skip k(ik,il)', ik, il, "wv2 = ", wv2
for k in range(1,nz+2):
ipsihat[k, :, :] = (fft.ifft2(ipsihat[k, :, :]))
if self.bottomboundary == 'psi=0':
self.psis = np.r_[(np.real(ipsihat)), np.zeros((1,ny,nx))]
else:
self.psis = np.real(ipsihat)
self.psis[0,:,:]= self.psis[1,:,:]
self.psis[-1,:,:]=self.psis[-2,:,:]-self.dzc[-1]*np.real(fft.ifft2(-bhats))/self.f0
self.rhos = self.psi2rho(self.psis)
self.us, self.vs = psi2uv(self.lon, self.lat, self.psis)
return
def calcFft(self):
"""Calculate the 2d FFT of the image (self.fimage).
If 'shift', adds a shift to move the small spatial scales to the
center of the FFT image to self.fimage. Also calculates the frequencies. """
# Generate the FFT (note, scipy places 0 - largest spatial scale frequencies - at corners)
self.fimage = fftpack.fft2(self.image)
if self.shift:
# Shift the FFT to put the largest spatial scale frequencies at center
self.fimage = fftpack.fftshift(self.fimage)
# Note, these frequencies follow unshifted order (0= first, largest spatial scale (with positive freq)).
self.xfreq = fftpack.fftfreq(self.nx, 1.0)
self.yfreq = fftpack.fftfreq(self.ny, 1.0)
self.xfreqscale = self.xfreq[1] - self.xfreq[0]
self.yfreqscale = self.yfreq[1] - self.yfreq[0]
return
def __init__(self, shape, space):
"docstring"
nx, ny = shape
dx, dy = space
scal_y = 2 * pi / dy / ny
scal_x = 2 * pi / dx / nx
k = fftfreq(nx, 1 / nx)[:, None] * 1j * scal_x
l = fftfreq(ny, 1 / ny)[None, :] * 1j * scal_y
lapl = k**2 + l**2
lapl[0, 0] = 1.0
self.k, self.l, self.lapl = k, l, lapl
def __init__(self, raw_files, blocksize, samplerate, fedge, fedge_at_top,
time_offset=0.0*u.s, dtype='cu4bit,cu4bit', comm=None):
"""ARO data aqcuired with a CHIME correlator containts 1024 channels
over the 400MHz BW, 2 polarizations, and 2 unsigned 8-byte ints for
real and imaginary for each timestamp.
"""
self.meta = eval(open(raw_files[0] + '.meta').read())
nchan = self.meta['nfreq']
self.time0 = Time(self.meta['stime'], format='unix') + time_offset
self.npol = self.meta['ninput']
self.samplerate = samplerate
self.fedge_at_top = fedge_at_top
if fedge.isscalar:
self.fedge = fedge
f = fftshift(fftfreq(nchan, (2./samplerate).to(u.s).value)) * u.Hz
if fedge_at_top:
self.frequencies = fedge - (f-f[0])
else:
self.frequencies = fedge + (f-f[0])
else:
assert fedge.shape == (nchan,)
self.frequencies = fedge
if fedge_at_top:
self.fedge = self.frequencies.max()
else:
self.fedge = self.frequencies.min()
self.dtsample = (nchan * 2 / samplerate).to(u.s)
if comm is None or comm.rank == 0:
print("In AROCHIMEData, calling super")
print("Start time: ", self.time0.iso)
super(AROCHIMEData, self).__init__(raw_files, blocksize, dtype, nchan,
comm=comm)
def _getFFT(self, data, fs):
"""
@param data:
set of samples
@param fs :
sample-rate of the data (samples/s)
"""
# Number of total samplepoints
N = len( data )
# Sample rate
T = 1.0 / fs # sample interval T = 1/256 = 0.0039 s
x = np.linspace(0.0, (N*T), N)
# frequency content
yfft = fft(data, N)
# let's take only the positive frequencies and normalize the amplitude
yfft = np.abs(yfft) / N
freqs = fftfreq(N, T)
half = int(np.floor(N/2)/2)
freqs = freqs[0:half]
yfft = [yfft[0]] + [ y * 2 for y in yfft[1:half] ]
return freqs, yfft
def band_hilbert(x, fs, band, N=None, axis=-1):
x = np.asarray(x)
Xf = fftpack.fft(x, N, axis=axis)
w = fftpack.fftfreq(x.shape[0], d=1. / fs)
Xf[(w < band[0]) | (w > band[1])] = 0
x = fftpack.ifft(Xf, axis=axis)
return 2*x
def stftfreq(wsize, sfreq=None): # noqa: D401
"""Frequencies of stft transformation.
Parameters
----------
wsize : int
Size of stft window
sfreq : float
Sampling frequency. If None the frequencies are given between 0 and pi
otherwise it's given in Hz.
Returns
-------
freqs : array
The positive frequencies returned by stft
See Also
--------
stft
istft
"""
n_freq = wsize // 2 + 1
freqs = fftfreq(wsize)
freqs = np.abs(freqs[:n_freq])
if sfreq is not None:
freqs *= float(sfreq)
return freqs
def get_power2(x, fs, band, n_sec=5):
n_steps = int(n_sec * fs)
w = fftpack.fftfreq(n_steps, d=1. / fs * 2)
print(len(range(0, x.shape[0] - n_steps, n_steps)))
pows = [2*np.sum(fftpack.rfft(x[k:k+n_steps])[(w > band[0]) & (w < band[1])]**2)/n_steps
for k in range(0, x.shape[0] - n_steps, n_steps)]
return np.array(pows)
def _mt_spectra(x, dpss, sfreq):
""" Compute tapered spectra
Parameters
----------
x : array, shape=(n_signals, n_times)
Input signal
dpss : array, shape=(n_tapers, n_times)
The tapers
sfreq : float
The sampling frequency
Returns
-------
x_mt : array, shape=(n_signals, n_tapers, n_times)
The tapered spectra
freqs : array
The frequency points in Hz of the spectra
"""
# remove mean (do not use in-place subtraction as it may modify input x)
x = x - np.mean(x, axis=-1)[:, np.newaxis]
x_mt = fftpack.fft(x[:, np.newaxis, :] * dpss)
# only keep positive frequencies
freqs = fftpack.fftfreq(x.shape[1], 1. / sfreq)
freq_mask = (freqs >= 0)
x_mt = x_mt[:, :, freq_mask]
freqs = freqs[freq_mask]
return x_mt, freqs
def _ajust_units(self):
"""
this must be called always that a change in the potential is made
because the interface to outside is always in eV, nm, s while
internally it works always with atomic units
"""
self.x_m = self.x_nm * 1.0e-9 # nm to m
self.x_au = self.x_m / self.au_l # m to au
self.dx_m = self.x_m[1]-self.x_m[0] # dx
self.dx_au = self.x_au[1]-self.x_au[0] # dx
self.k_au = fftfreq(self.N, d=self.dx_au)
self.v_j = self.v_ev * self.ev # ev to j
self.v_au_ti = self.v_au = self.v_j / self.au_e # j to au
# check whether there is any bias to apply
try:
self.v_au_ti += self.bias_au
except:
pass
# check whether there is any dynamic field to apply
try:
assert self.v_au_td and isinstance(self.v_au_td, LambdaType)
self.v_au_full = lambda t: self.v_au_ti + self.v_au_td(t)
except:
self.v_au_full = lambda t: self.v_au_ti
def analyzeSound(self):
""" highlights N first peaks in frequency diagram
"""
# on recharge les données
data = self.data
sample_freq = self.sample_freq
from scipy.fftpack import fftfreq
freq_vect = fftfreq(data.size) * sample_freq
# on trouve les maxima
y0 = abs(fft(data))
# y1 = abs(fft(data[:, 1]))
maxi0 = ((diff(sign(diff(y0))) < 0) & (y0[1:-1] > y0.max()/10.)).nonzero()[0] + 1 # local max
# maxi1 = ((diff(sign(diff(y1))) < 0) & (y1[1:-1] > y1.max()/10.)).nonzero()[0] + 1 # local max
# fréquence
ax = self.main_figure.figure.add_subplot(212)
ax.plot(freq_vect[maxi0], y0[maxi0], "o")
# ax.plot(freq_vect[maxi1], y1[maxi1], "o")
# annotations au dessus d'une fréquence de coupure
fc = 100
for point in maxi0[(freq_vect[maxi0] > fc).nonzero()][:self.ui.spinBox.value()]:
plt.annotate("%.2f" % freq_vect[point], (freq_vect[point], y0[point]))
# for point in maxi1[(freq_vect[maxi0] > fc).nonzero()][:self.ui.spinBox.value()]:
# plt.annotate("%.2f" % freq_vect[point], (freq_vect[point], y1[point]))
self.ui.main_figure.canvas.draw()
def __init__(self, waveReader):
self.windowSize = PADDED_WINDOW_SAMPLES
self.sampleRate = waveReader.samplerate
self.signal = waveReader.channels[0]
# Performs STFT on samples
pspc = self.stft(WINDOW_SAMPLES, HOP_SAMPLES)
# Gets FFT bins center frequencies, discard negative frequencies
freqs = fftfreq(
self.windowSize,
float(1)/waveReader.samplerate
)[:self.windowSize/2]
# Scales bins according to the Terhardt transfer function
pspc = self.scaleTerhardt(pspc, freqs)
# Warps frequencies to bark bins
pspc = self.scaleBark(pspc, freqs)
# Convolves frequency envelopes with a half-hanning window
pspc = self.temporalMask(pspc)
# Scales samples to dB with I0 = 60, clips values below -60dB
pspc = self.scaleDb(pspc)
self.spectogram = pspc
self.eventDetection = self.calculateEventDetection(self.spectogram)
self.eventDetectionEvents = self.findEvents(self.eventDetection)
self.loudness = self.calculateLoudness(self.spectogram)
self.events = self.matchEventsToLoudness(self.eventDetectionEvents, self.loudness)
self.eventSamples = self.events * HOP_SAMPLES
data = np.loadtxt("monthrg.dat")
agnios = np.array(data[:, 0])
manchas = np.array(data[:, 3])
dias = np.array(data[:, 2])
meses = np.array(data[:, 1])
i = dias > 0
#Angios y manchas por agnio
t = agnios[i] + meses[i] / 12
manchas_agnios = manchas[i]
#Agnios y manchas desde 1900
ii = t > 1850
year = t[ii]
manch = manchas_agnios[ii]
plt.plot(year, manch)
plt.savefig("manchas2.png")
plt.close()
#transformadas de fourier para los datos anteriores
dt = 1.0 #Unidades: 1/meses
fourier = fft(manch) / len(year)
frecuencia = fftfreq(len(year), dt)
plt.plot(frecuencia, abs(fourier))
plt.savefig("frecuencia.png")
plt.close()
#Busca la frecuencia
iii = frecuencia > 0
indice = np.argmax(fourier[iii])
f = frecuencia[iii]
frec_max = f[indice]
t = 1 / frec_max
print "El periodo es", t, "meses"
def _spectral_helper(x, y, fs=1.0, window='hanning', nperseg=256,
noverlap=None, nfft=None, detrend='constant',
return_onesided=True, scaling='spectrum', axis=-1,
mode='psd'):
"""
Calculate various forms of windowed FFTs for PSD, CSD, etc.
This is a helper function that implements the commonality between the
psd, csd, and spectrogram functions. It is not designed to be called
externally. The windows are not averaged over; the result from each window
is returned.
Parameters
---------
x : array_like
Array or sequence containing the data to be analyzed.
y : array_like
Array or sequence containing the data to be analyzed. If this is
the same object in memoery as x (i.e. _spectral_helper(x, x, ...)),
the extra computations are spared.
fs : float, optional
Sampling frequency of the time series. Defaults to 1.0.
window : str or tuple or array_like, optional
Desired window to use. See `get_window` for a list of windows and
required parameters. If `window` is array_like it will be used
directly as the window and its length will be used for nperseg.
Defaults to 'hanning'.
nperseg : int, optional
Length of each segment. Defaults to 256.
noverlap : int, optional
Number of points to overlap between segments. If None,
``noverlap = nperseg // 2``. Defaults to None.
nfft : int, optional
Length of the FFT used, if a zero padded FFT is desired. If None,
the FFT length is `nperseg`. Defaults to None.
detrend : str or function or False, optional
Specifies how to detrend each segment. If `detrend` is a string,
it is passed as the ``type`` argument to `detrend`. If it is a
function, it takes a segment and returns a detrended segment.
If `detrend` is False, no detrending is done. Defaults to 'constant'.
return_onesided : bool, optional
If True, return a one-sided spectrum for real data. If False return
a two-sided spectrum. Note that for complex data, a two-sided
spectrum is always returned.
scaling : { 'density', 'spectrum' }, optional
Selects between computing the cross spectral density ('density')
where `Pxy` has units of V**2/Hz and computing the cross spectrum
('spectrum') where `Pxy` has units of V**2, if `x` and `y` are
measured in V and fs is measured in Hz. Defaults to 'density'
axis : int, optional
Axis along which the periodogram is computed; the default is over
the last axis (i.e. ``axis=-1``).
mode : str, optional
Defines what kind of return values are expected. Options are ['psd',
'complex', 'magnitude', 'angle', 'phase'].
Returns
-------
freqs : ndarray
Array of sample frequencies.
result : ndarray
Array of output data, contents dependant on *mode* kwarg.
t : ndarray
Array of times corresponding to each data segment
References
----------
.. [1] Stack Overflow, "Rolling window for 1D arrays in Numpy?",
http://stackoverflow.com/a/6811241
.. [2] Stack Overflow, "Using strides for an efficient moving average
filter", http://stackoverflow.com/a/4947453
Notes
-----
Adapted from matplotlib.mlab
.. versionadded:: 0.16.0
"""
if mode not in ['psd', 'complex', 'magnitude', 'angle', 'phase']:
raise ValueError("Unknown value for mode %s, must be one of: "
"'default', 'psd', 'complex', "
"'magnitude', 'angle', 'phase'" % mode)
# If x and y are the same object we can save ourselves some computation.
same_data = y is x
if not same_data and mode != 'psd':
raise ValueError("x and y must be equal if mode is not 'psd'")
axis = int(axis)
# Ensure we have np.arrays, get outdtype
x = np.asarray(x)
if not same_data:
y = np.asarray(y)
outdtype = np.result_type(x,y,np.complex64)
else:
outdtype = np.result_type(x,np.complex64)
if not same_data:
# Check if we can broadcast the outer axes together
xouter = list(x.shape)
youter = list(y.shape)
xouter.pop(axis)
youter.pop(axis)
try:
outershape = np.broadcast(np.empty(xouter), np.empty(youter)).shape
except ValueError:
raise ValueError('x and y cannot be broadcast together.')
if same_data:
if x.size == 0:
return np.empty(x.shape), np.empty(x.shape), np.empty(x.shape)
else:
if x.size == 0 or y.size == 0:
outshape = outershape + (min([x.shape[axis], y.shape[axis]]),)
emptyout = np.rollaxis(np.empty(outshape), -1, axis)
return emptyout, emptyout, emptyout
if x.ndim > 1:
if axis != -1:
x = np.rollaxis(x, axis, len(x.shape))
if not same_data and y.ndim > 1:
y = np.rollaxis(y, axis, len(y.shape))
# Check if x and y are the same length, zero-pad if neccesary
if not same_data:
if x.shape[-1] != y.shape[-1]:
if x.shape[-1] < y.shape[-1]:
pad_shape = list(x.shape)
pad_shape[-1] = y.shape[-1] - x.shape[-1]
x = np.concatenate((x, np.zeros(pad_shape)), -1)
else:
pad_shape = list(y.shape)
pad_shape[-1] = x.shape[-1] - y.shape[-1]
y = np.concatenate((y, np.zeros(pad_shape)), -1)
# X and Y are same length now, can test nperseg with either
if x.shape[-1] < nperseg:
warnings.warn('nperseg = {0:d}, is greater than input length = {1:d}, '
'using nperseg = {1:d}'.format(nperseg, x.shape[-1]))
nperseg = x.shape[-1]
nperseg = int(nperseg)
if nperseg < 1:
raise ValueError('nperseg must be a positive integer')
if nfft is None:
nfft = nperseg
elif nfft < nperseg:
raise ValueError('nfft must be greater than or equal to nperseg.')
else:
nfft = int(nfft)
if noverlap is None:
noverlap = nperseg//2
elif noverlap >= nperseg:
raise ValueError('noverlap must be less than nperseg.')
else:
noverlap = int(noverlap)
# Handle detrending and window functions
if not detrend:
def detrend_func(d):
return d
elif not hasattr(detrend, '__call__'):
def detrend_func(d):
return signaltools.detrend(d, type=detrend, axis=-1)
elif axis != -1:
# Wrap this function so that it receives a shape that it could
# reasonably expect to receive.
def detrend_func(d):
d = np.rollaxis(d, -1, axis)
d = detrend(d)
return np.rollaxis(d, axis, len(d.shape))
else:
detrend_func = detrend
if isinstance(window, string_types) or type(window) is tuple:
win = get_window(window, nperseg)
else:
win = np.asarray(window)
if len(win.shape) != 1:
raise ValueError('window must be 1-D')
if win.shape[0] != nperseg:
raise ValueError('window must have length of nperseg')
if np.result_type(win,np.complex64) != outdtype:
win = win.astype(outdtype)
if mode == 'psd':
if scaling == 'density':
scale = 1.0 / (fs * (win*win).sum())
elif scaling == 'spectrum':
scale = 1.0 / win.sum()**2
else:
raise ValueError('Unknown scaling: %r' % scaling)
else:
scale = 1
if return_onesided is True:
if np.iscomplexobj(x):
sides = 'twosided'
else:
sides = 'onesided'
if not same_data:
if np.iscomplexobj(y):
sides = 'twosided'
else:
sides = 'twosided'
if sides == 'twosided':
num_freqs = nfft
elif sides == 'onesided':
if nfft % 2:
num_freqs = (nfft + 1)//2
else:
num_freqs = nfft//2 + 1
# Perform the windowed FFTs
result = _fft_helper(x, win, detrend_func, nperseg, noverlap, nfft)
result = result[..., :num_freqs]
freqs = fftpack.fftfreq(nfft, 1/fs)[:num_freqs]
if not same_data:
# All the same operations on the y data
result_y = _fft_helper(y, win, detrend_func, nperseg, noverlap, nfft)
result_y = result_y[..., :num_freqs]
result = np.conjugate(result) * result_y
elif mode == 'psd':
result = np.conjugate(result) * result
elif mode == 'magnitude':
result = np.absolute(result)
elif mode == 'angle' or mode == 'phase':
result = np.angle(result)
elif mode == 'complex':
pass
result *= scale
if sides == 'onesided':
if nfft % 2:
result[...,1:] *= 2
else:
# Last point is unpaired Nyquist freq point, don't double
result[...,1:-1] *= 2
t = np.arange(nperseg/2, x.shape[-1] - nperseg/2 + 1, nperseg - noverlap)/float(fs)
if sides != 'twosided' and not nfft % 2:
# get the last value correctly, it is negative otherwise
freqs[-1] *= -1
# we unwrap the phase here to handle the onesided vs. twosided case
if mode == 'phase':
result = np.unwrap(result, axis=-1)
result = result.astype(outdtype)
# All imaginary parts are zero anyways
if same_data and mode != 'complex':
result = result.real
# Output is going to have new last axis for window index
if axis != -1:
# Specify as positive axis index
if axis < 0:
axis = len(result.shape)-1-axis
# Roll frequency axis back to axis where the data came from
result = np.rollaxis(result, -1, axis)
else:
# Make sure window/time index is last axis
result = np.rollaxis(result, -1, -2)
return freqs, t, result
factor = input()
factor = int(factor)
ax = plt.gca()
data_test = 2050
data_over = 329
time_test = np.arange(1*10**(-9), data_test*4*10**(-9), 4*10**(-9))
data_array = np.load('ratio.npz')
ratio = data_array['x']
angle_dif = data_array['y']
dt = 4*10**(-9)
freq_fft_test = fftfreq(data_test, dt)
freq_fft_test_plus = freq_fft_test[0:data_test//2]
freq_array = np.arange(1*10**6, 41*10**6, 1*10**6)
freq_interpolate = np.arange(0, 41*10**6, 0.5*10**6)
func_amp = interpolate.InterpolatedUnivariateSpline(freq_array, ratio, k = 1)
func_angle = interpolate.InterpolatedUnivariateSpline(freq_array, angle_dif, k = 1)
result_amp_test = func_amp(freq_fft_test_plus)
for i in range(data_over, data_test//2):
result_amp_test[i] = result_amp_test[data_over-1]
result_amp_test_min = result_amp_test[data_over-1]
result_angle_test = func_angle(freq_fft_test_plus)
for i in range(data_over, data_test//2):
def select_prd_peak(wl, data, window=None, axes=None, known_prd=None):
assert len(data.shape) == 1, 'expected spectrum averaged over ' +\
'camera frames'
threshold = 0.001 # fraction of DC peak
window_width = 150 # in pixels
pad_factor = 1
adjacent_pts_fit = 2 # fit on either side
min_prd = 650 # fs
dc_left_time, dc_right_time = -200., 200. # in fs
if window:
window_width = window.shape[0]
raise NotImplementedError('untested implementation for reusing window')
else:
window = get_window(('kaiser', 7), window_width, fftbins=False)
assert window.shape[0] < data.shape[0], 'window must be smaller than data'
assert len(data.shape) == 1, 'data should be 1d'
freq, data, df = wavelen_to_freq(wl, data, ret_df=True)
padded = np.zeros((data.shape[0] * pad_factor, ))
padded[:data.shape[0]] = data * get_window(('kaiser', 20), data.shape[0])
time = fftshift(fftfreq(padded.shape[0], df))
ft = fftshift(ifft(padded))
ft_abs = np.abs(ft)
if known_prd is None:
res = argrelmax(ft_abs, order=20 * pad_factor)[0]
prd_idx = res[np.logical_and(
time[res] > min_prd, ft_abs[res] > threshold * np.max(ft_abs))][0]
# fit parabola to adjacent points to find intrabin time
sel = slice(prd_idx - adjacent_pts_fit, prd_idx + adjacent_pts_fit)
p = np.polyfit(time[sel], ft_abs[sel], 2)
prd_guess = -0.5 * p[1] / p[0] # from vertex form
log.debug('found PRD at {:.1f} fs'.format(prd_guess))
else:
prd_guess = known_prd
prd_idx = np.abs(time - prd_guess).argmin()
log.debug('reusing PRD at {:.1f} fs, idx {:d}'.format(
time[prd_idx], prd_idx))
if axes:
# going to plot stuff to axes
axes.plot(time, ft_abs, marker='+', markersize=5)
next_highest = ft_abs[prd_idx]
axes.text(prd_guess, next_highest, r'${:5.2f}$'.format(prd_guess))
axes.set_ylim(0, 1.1 * next_highest)
axes.vlines(prd_guess, 0, next_highest, color='r')
sel_peak = slice(prd_idx - window_width // 2, prd_idx + window_width // 2)
lo_peak = np.zeros_like(ft)
lo_peak[sel_peak] = ft[sel_peak] * window
if axes:
axes.plot(time, abs(lo_peak))
# detect minima near DC peak
# first find index of pm 60 fs, and call that the DC interval
dc_left_idx, dc_right_idx = np.abs(time - dc_left_time).argmin(), \
np.abs(time-dc_right_time).argmin()
sel_dc = slice(dc_left_idx, dc_right_idx)
dc_peak = np.zeros_like(ft)
dc_peak[sel_dc] = ft[sel_dc] * get_window(
('kaiser', 7), dc_right_idx - dc_left_idx)
if axes:
axes.plot(time, np.abs(dc_peak), 'c', linewidth=1.2)
dt = np.abs(time[1] - time[0])
freq = np.linspace(freq[0], freq[-1], freq.shape[0] * pad_factor)
# estimate of E_LO(w) without phase information
E_lo = np.sqrt(np.abs(fft(dc_peak)))
E_sig = np.exp(-1j * prd_guess * freq) * fft(lo_peak) / E_lo
return prd_guess, freq, E_sig, E_lo
# 1. Get the window profile
window = get_window('hamming', N_window)
# 2. Set up the FFT
result = []
start = 0
while (start < N_data - N_window):
end = start + N_window
result.append(fftshift(fft(window*data[start:end])))
start = end
result.append(fftshift(fft(window*data[-N_window:])))
result = array(result,result[0].dtype)
# Display results
freqscale = fftshift(fftfreq(N_window,dT))[150:-150]/1e3
figure(1)
clf()
imshow(abs(result[:,150:-150]), extent=(freqscale[-1], freqscale[0],
(N_data*dT - T_window/2.0), T_window/2.0))
xlabel('Frequency (kHz)')
ylabel('Time (sec.)')
gray()
show()
def resample(x, num, t=None, axis=0, window=None):
"""
Resample `x` to `num` samples using Fourier method along the given axis.
The resampled signal starts at the same value as `x` but is sampled
with a spacing of ``len(x) / num * (spacing of x)``. Because a
Fourier method is used, the signal is assumed to be periodic.
Parameters
----------
x : array_like
The data to be resampled.
num : int
The number of samples in the resampled signal.
t : array_like, optional
If `t` is given, it is assumed to be the sample positions
associated with the signal data in `x`.
axis : int, optional
The axis of `x` that is resampled. Default is 0.
window : array_like, callable, string, float, or tuple, optional
Specifies the window applied to the signal in the Fourier
domain. See below for details.
Returns
-------
resampled_x or (resampled_x, resampled_t)
Either the resampled array, or, if `t` was given, a tuple
containing the resampled array and the corresponding resampled
positions.
Notes
-----
The argument `window` controls a Fourier-domain window that tapers
the Fourier spectrum before zero-padding to alleviate ringing in
the resampled values for sampled signals you didn't intend to be
interpreted as band-limited.
If `window` is a function, then it is called with a vector of inputs
indicating the frequency bins (i.e. fftfreq(x.shape[axis]) ).
If `window` is an array of the same length as `x.shape[axis]` it is
assumed to be the window to be applied directly in the Fourier
domain (with dc and low-frequency first).
For any other type of `window`, the function `scipy.signal.get_window`
is called to generate the window.
The first sample of the returned vector is the same as the first
sample of the input vector. The spacing between samples is changed
from dx to:
dx * len(x) / num
If `t` is not None, then it represents the old sample positions,
and the new sample positions will be returned as well as the new
samples.
"""
x = asarray(x)
X = fft(x, axis=axis)
Nx = x.shape[axis]
if window is not None:
if callable(window):
W = window(fftfreq(Nx))
elif isinstance(window, ndarray) and window.shape == (Nx, ):
W = window
else:
W = ifftshift(get_window(window, Nx))
newshape = ones(len(x.shape))
newshape[axis] = len(W)
W.shape = newshape
X = X * W
sl = [slice(None)] * len(x.shape)
newshape = list(x.shape)
newshape[axis] = num
N = int(np.minimum(num, Nx))
Y = zeros(newshape, 'D')
sl[axis] = slice(0, (N + 1) / 2)
Y[sl] = X[sl]
sl[axis] = slice(-(N - 1) / 2, None)
Y[sl] = X[sl]
y = ifft(Y, axis=axis) * (float(num) / float(Nx))
if x.dtype.char not in ['F', 'D']:
y = y.real
if t is None:
return y
else:
new_t = arange(0, num) * (t[1] - t[0]) * Nx / float(num) + t[0]
return y, new_t
def direct_hilbert(x):
fx = fft(x)
n = len(fx)
w = fftfreq(n) * n
w = 1j * sign(w)
return ifft(w * fx)
import scipy.io.wavfile as wavfile
import scipy
import scipy.fftpack as fftpk
import numpy as np
from matplotlib import pyplot as plt
s_rate, signal = wavfile.read("tibet.wav")
FFT = abs(scipy.fft(signal))
freqs = fftpk.fftfreq(len(FFT), (1.0 / s_rate))
plt.plot(freqs[range(len(FFT) // 2)], FFT[range(len(FFT) // 2)])
plt.xlabel('Frequency (Hz)')
plt.ylabel('Amplitude')
plt.show()
def plot_shh_anal_loc():
"""
Function to plot multiple analytical power spectra along e.g. an aquifer in a 3D plot.
Still not working because plot3d has issues with log scale ...
"""
# set parameters
data_points = 8000
time_step_size = 86400
aquifer_length = 1000
Sy = 1e-1
T = 0.001
from calc_tc import calc_tc
tc = calc_tc(aquifer_length, Sy, T)
print(tc)
import sys
# add search path for own modules
sys.path.append("/Users/houben/PhD/python/scripts/spectral_analysis")
from shh_analytical import shh_analytical
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D
import scipy.fftpack as fftpack
# create an input signal
np.random.seed(123456789)
input = np.random.rand(data_points)
spectrum = fftpack.fft(input)
# erase first half of spectrum
spectrum = abs(spectrum[:round(len(spectrum) / 2)])**2
spectrum = spectrum # [1:]
# X contains the different locations
X = np.linspace(0, aquifer_length - 1, 10)
X = [100, 900]
# Y contains the frequencies, erase first data point because it's 0
Y = abs(fftpack.fftfreq(len(input),
time_step_size))[:round(len(input) / 2)]
Y = np.log10(Y[1:])
Z = np.zeros((len(Y), len(X)))
for i, loc in enumerate(X):
Z[:, i] = np.log10(
shh_analytical((Y, spectrum),
Sy=Sy,
T=T,
x=loc,
L=aquifer_length,
m=5,
n=5,
norm=False))
# erase first data point from Z for each location
print(Z)
print(Y)
import matplotlib.pyplot as plt
plt.plot(Y, Z[:, 0])
# plt.loglog(Y,Z[:,0])
# X, Y = np.meshgrid(X, Y)
# fig = plt.figure()
# ax = Axes3D(fig)
# surf = ax.plot_surface(
# X, Y, Z, rstride=1, cstride=2, shade=False, linewidth=1, cmap="Spectral_r"
# )
# surf = ax.plot_wireframe(X, Y, Z, rstride=0, cstride=1, cmap=cm.magma)
# surf.set_edgecolors(surf.to_rgba(surf._A))
# surf.set_facecolors("white")
# ax1 = ax.plot_wireframe(X, Y, Z, rstride=1, cstride=0)
# ax.set_xlabel("Location [m]")
# ax.set_ylabel("Frequency [Hz]")
# ax.set_zlabel("log Spectral Density")
# ax.set_zscale("log")
# ax.yaxis.set_scale("log")
# ax.zaxis._set_scale('log')
# ax.set_yscale("log")
plt.show()
def trialfunction(input_data):
trials_dic = {}
dbc = 0
if Alc_train_extractor.shape == Con_train_extractor.shape:
print('Same shape error:')
print(X_train.shape)
print(y_train.shape)
raise SystemExit
if (input_data.shape == Alc_train_extractor.shape) or (
input_data.shape
== Alc_train_classifier.shape) or (input_data.shape
== Alc_test.shape):
dbc = EEG_data
if (input_data.shape == Con_train_extractor.shape) or (
input_data.shape
== Con_train_classifier.shape) or (input_data.shape
== Con_test.shape):
dbc = EEG_data_control
for pos in input_data:
Trial = dbc.loc[dbc['trial number'] == pos]
columns = ['channel', 'time', 'sensor value']
Trial = Trial.pivot_table(index='channel',
columns='time',
values='sensor value')
trials_dic[pos] = Trial
RGB_dic = {}
for key in trials_dic:
data = trials_dic.get(key)
# Get real amplitudes of FFT (only in postive frequencies)
fft_raw = fft(data)
fft_vals = np.absolute(fft_raw)
fft_vals = normalize(fft_vals, axis=1)
# Get frequencies for amplitudes in Hz
fs = 256 # Sampling rate
fft_freq = fftfreq(fs, 1.0 / fs)
# Define EEG bands
eeg_bands = {
'Theta': (4, 7),
'Alpha': (8, 12),
'Beta': (13, 30),
}
# Take the sum of squared absolute values/amplitudes for each EEG band
eeg_band_fft = defaultdict(list)
for band in eeg_bands:
freq_ix = np.where((fft_freq >= eeg_bands[band][0])
& (fft_freq <= eeg_bands[band][1]))[0]
for channel in fft_vals:
filterdch = channel[freq_ix]
sqdvals = np.square(filterdch)
sumvals = np.sum(sqdvals, axis=0)
eeg_band_fft[band].append(sumvals)
extracted_df = pd.DataFrame(eeg_band_fft)
neeg = EEG_data.drop(columns=[
'matching condition', 'name', 'trial number', 'subject identifier',
'time', 'sample num', 'sensor value'
])
neeg = neeg.drop_duplicates()
#get names of source elctrodes:
extracted_df = extracted_df.reset_index(drop=True)
neeg = neeg.reset_index(drop=True)
e_names = neeg
e_names = e_names.rename(columns={'sensor position': 0})
extracted_df = extracted_df.join(neeg)
#get coordinates in 3d from robertoostenveld.nl/electrodes/plotting_1005.txt
coords = pd.read_csv(
'/kaggle/input/httpsrobertoostenveldnlelectrodes/plotting_1005.txt',
sep='\t',
header=None)
coords = coords.drop(coords.columns[4], axis=1)
#print(coords)
testerd = pd.merge(e_names, coords, on=0, how='inner')
testerd.set_index('channel', inplace=True)
testerd.columns = ['pos', 'x', 'y', 'z']
extracted_df = extracted_df.rename(columns={'sensor position': "pos"})
#filter values and coordinates
extracted_df = pd.merge(extracted_df, testerd, on="pos", how='inner')
extracted_df = extracted_df.drop(['x', 'y', 'z'], axis=1)
extracted_df.set_index('channel', inplace=True)
extracted_df = extracted_df.drop(columns=['pos'])
extracted_df.index.names = ['pos']
#adapted from https://www.samuelbosch.com/2014/02/azimuthal-equidistant-projection.html
class Point(object):
def __init__(self, x, y, z):
self.x = x
self.y = y
self.z = z
class AzimuthalEquidistantProjection(object):
"""
http://mathworld.wolfram.com/AzimuthalEquidistantProjection.html
http://mathworld.wolfram.com/SphericalCoordinates.html
"""
def __init__(self):
self.t1 = pi / 2 ## polar latitude center of projection , https://en.wikipedia.org/wiki/Azimuthal_equidistant_projection
self.l0 = 0 ## arbitrary longitude center of projection
self.cost1 = cos(self.t1)
self.sint1 = sin(self.t1)
def project(self, point):
#ADDAPTED FOR 3D CARTESIAN TO SPHERICAL
hxy = np.hypot(point.x, point.y)
t = np.arctan2(point.z, hxy)
l = np.arctan2(point.y, point.x)
###
costcosll0 = cos(t) * cos(l - self.l0)
sint = sin(t)
c = acos((self.sint1) * (sint) + (self.cost1) * costcosll0)
k = c / sin(c)
x = k * cos(t) * sin(l - self.l0)
y = k * (self.cost1 * sint - self.sint1 * costcosll0)
return x, y
#Projection df
projected_df = pd.DataFrame()
for index, row in testerd.iterrows():
x = row['x']
y = row['y']
z = row['z']
p = AzimuthalEquidistantProjection()
r = p.project(Point(x, y, z))
r = pd.Series(r)
projected_df = projected_df.append(r, ignore_index=True)
projected_df = projected_df.rename(columns={0: 'X', 1: 'Y'})
###map coodinate with valuies
new_df = projected_df.join(extracted_df)
new_df = new_df.drop([31]) # drop row because i contains no values
#print(new_df)
Theta_df = new_df.drop(['Alpha', 'Beta', 'X', 'Y'], axis=1)
Alpha_df = new_df.drop(['Theta', 'Beta', 'X', 'Y'], axis=1)
Beta_df = new_df.drop(['Theta', 'Alpha', 'X', 'Y'], axis=1)
#map onto mesh
xpoints = np.array(new_df[['X']].squeeze())
ypoints = np.array(new_df[['Y']].squeeze())
Thetavalues = np.array(Theta_df).squeeze()
Alphavalues = np.array(Alpha_df).squeeze()
Betavalues = np.array(Beta_df).squeeze()
xx, yy = np.mgrid[-1.5:1.5:32j, -1.5:1.5:32j]
Thetavalues = minmax_scale(Thetavalues,
feature_range=(0.0, 1.0),
axis=0)
Alphavalues = minmax_scale(Alphavalues,
feature_range=(0.0, 1.0),
axis=0)
Betavalues = minmax_scale(Betavalues, feature_range=(0.0, 1.0), axis=0)
Thetagrid = griddata((xpoints, ypoints),
Thetavalues, (xx, yy),
method='cubic',
fill_value=0.0)
Alphagrid = griddata((xpoints, ypoints),
Alphavalues, (xx, yy),
method='cubic',
fill_value=0.0)
Betagrid = griddata((xpoints, ypoints),
Betavalues, (xx, yy),
method='cubic',
fill_value=0.0)
##RGB construction
RGB = np.empty((32, 32, 3))
RGB[:, :, 0] = Thetagrid
RGB[:, :, 1] = Alphagrid
RGB[:, :, 2] = Betagrid
RGB_dic[key] = RGB
##creating new dict with new keys
lendict = len(RGB_dic)
#print('lendict: ',lendict)
lenlist = np.arange(0, lendict)
#print(lenlist)
final_dict = dict(zip(lenlist, list(RGB_dic.values())))
return final_dict
def fourier_transform(funcs, dts, inSI=False, SI_units='thz',
convention='math', zero_padding=False, npow=1,
**kwargs_norm_units):
"""
The F.T. of an array with various sampling times for each of the funcs
Input
-----
funcs : a list of np.array types representing the discrete time signal.
I assume you have correctly sampled the funcs by not including the endpoint
of the time signal
Must be casted as list so enclose with []. Or as a tuple like (f1,) with the comma being important. CAST AS A TUPLE
dts : the sampling time step. For now, every function has the same time step.
inSI (optional) : wheteher to use SI units or normalized units for frequency (Default: False)
SI_units (optional) : specify the SI unit for frequency. (Default: THz). Valid options are 'thz',
**kwargs_norm_units (optional) : If inSI==True, then specify the appropriate normalized units for
the toSI function. Please see docstring for toSI for further details.
convention: 'physics' convention or 'math' convention. Physics convention uses
ifft as Fourer transform and math convention uses fft
Returns
-------
(frequencies, fft of signal) : list containing the frequencies and
spectrum with the zero frequency centered
else (Default)
Return nothing
"""
if isinstance(dts, float):
dts = np.tile(dts, len(funcs)) # cast as a list
elif isinstance(dts, list):
if len(dts) != len(funcs):
print('The funcs and dts array are not the same size.')
return None
funcs_freq = []
freqs_list = []
for (f, dt) in zip(funcs, dts):
Ns = np.size(f)
# windowing
# window_real = np.max(np.real(f))*signal.hann(Ns)
# window_imag = np.max(np.imag(f))*signal.hann(Ns)
# Testing window
# plt.figure()
# plt.plot(window)
# plt.plot(np.abs(f))
# plt.show()
# plt.close()
# f = window*f
# f = window_real*np.real(f) + I*window_imag*np.imag(f)
if zero_padding:
NFFT = nextpow2(Ns, npow=npow)
# pad asymmetrical on right side, assumes sampling in [0,T)
# f = np.append(f, np.zeros(NFFT-Ns))
# f = np.pad(f, (0, NFFT-Ns), 'constant', constant_values=(0, 0))
# pad symmetrically on both sides since it's a gaussian. sampling [-0.5*T, 0.5*T)
Nleft = int(np.ceil(0.5*(NFFT - Ns)))
Nright = int((NFFT - Ns) - Nleft)
f = np.pad(f, (Nleft, Nright), 'constant', constant_values=(0, 0))
Ns = np.size(f)
# ipdb.set_trace()
if convention == 'math':
f_freq = fftshift((fft(f)))
elif convention == 'physics':
# f_freq = fftshift((ifft(f, n=2**15))) # another exaple of asymmetric padding on the right side
# Ns = np.size(f_freq)
f_freq = fftshift((ifft(f)))
freqs = fftshift(fftfreq(Ns, dt))
funcs_freq.append(f_freq)
freqs_list.append(freqs)
if inSI == True:
freqs = toSI(freqs, 'freq', SI_units, **kwargs_norm_units)
if freqs == None:
print('toSI function call failed. Aborting')
return None
return (freqs_list, funcs_freq)
# Reading the generated data signal in CSV format
df = pd.read_csv('test_sig_3.csv', header=0)
# Setting Number of Samples and Period
N = len(df)
T = (df.iloc[-1][0] - df.iloc[0][0]) / (N - 1)
print("Numbers of Samples (N):", N, " | Sampling Interval (T):", T)
# Obtaining the Values as a Numpy Array from the Dataframe
x = df['N'].values
y = df['F(N)'].values
print("Current DC Offset:", y.mean())
# Computing Fast Fourier Transform of Signal N, F(N)
xf = fftpack.fftfreq(N) / T
yf = fftpack.fft(y) * (2.0 / N)
# Setting the plotting parameters
xf_plot, yf_magplot, yf_phaseplot = np.linspace(0.0, 1.0 / (2 * T), num=N //
2), np.abs(yf[:N // 2]),
np.angle(yf[:N // 2])
# Reconstructing Sinusoidal Signal
y_recon = fftpack.ifft(yf) / (2.0 / N)
# Run the given data through the Savitzky-Golay Filter
filtered = savgol_filter(y, 101, 1)
# Create an array to place the different anomalies outside the bands
anom = []
print('\nloading:\n')
print(filetoopen)
data = stlab.readdata.readdat(filetoopen)
#data = [stlab.readdata.readdat(path) for path in pathlist]
Q = data[0]['Q ()'][0]
freq = []
volt_fft = []
current = []
for line in data:
time = line['Time (wp*t)']
voltage = line['AC Voltage (V)']
current.append(line['Current (Ic)'][0])
#testplot(time,voltage)
F = fftfreq(len(time), d=time[1] - time[0])
F = F[:len(F) // 2]
signal_fft = fft(voltage)
signal_fft = signal_fft[:len(signal_fft) // 2]
#testplot(F,abs(signal_fft))
freq.append(F)
volt_fft.append(abs(signal_fft))
freq = np.asarray(freq[0])
volt_fft = np.asarray(volt_fft)
peakfreqs = [
peakidx(np.log(volt_fft[i] + 1e-11), thres=0.1)
for i in range(len(data))
]
import numpy as np
from scipy.fftpack import fftfreq
from numpy.fft import fft
from matplotlib import pyplot as plt
from scipy.io import loadmat
from os.path import dirname
from likefunctions_boston import plotlikeconfig
plotlikeconfig(title='FFT', xlabel='Frequency(Hz)', ylabel='Strength')
samples = 1200
x = np.linspace(0, 1, samples)
data_bearing = np.zeros(samples * 3)
data_bearing[:samples] = 2 * np.sin(2 * np.pi * 200 * x) + 2 * np.sin(
2 * np.pi * 100 * x)
fft_data_bearing = fft(data_bearing)
# real_fft_data_bearing=rfft(data_bearing)
freq_fft_data_bearing = fftfreq(fft_data_bearing.size, 1 / samples)
freq_limit = int(fft_data_bearing.size / 2)
signal_limit = freq_limit
plt.stem(freq_fft_data_bearing[:freq_limit],
abs(fft_data_bearing[:freq_limit]),
linefmt='',
use_line_collection=True)
# plt.stem(freq_fft_data_bearing[:freq_limit],abs(real_fft_data_bearing)[:freq_limit],use_line_collection=True)
plt.show()
def iradon(radon_image,
theta=None,
output_size=None,
filter="ramp",
interpolation="linear",
circle=True):
"""
Inverse radon transform.
Reconstruct an image from the radon transform, using the filtered
back projection algorithm.
Parameters
----------
radon_image : array_like, dtype=float
Image containing radon transform (sinogram). Each column of
the image corresponds to a projection along a different angle. The
tomography rotation axis should lie at the pixel index
``radon_image.shape[0] // 2`` along the 0th dimension of
``radon_image``.
theta : array_like, dtype=float, optional
Reconstruction angles (in degrees). Default: m angles evenly spaced
between 0 and 180 (if the shape of `radon_image` is (N, M)).
output_size : int, optional
Number of rows and columns in the reconstruction.
filter : str, optional
Filter used in frequency domain filtering. Ramp filter used by default.
Filters available: ramp, shepp-logan, cosine, hamming, hann.
Assign None to use no filter.
interpolation : str, optional
Interpolation method used in reconstruction. Methods available:
'linear', 'nearest', and 'cubic' ('cubic' is slow).
circle : boolean, optional
Assume the reconstructed image is zero outside the inscribed circle.
Also changes the default output_size to match the behaviour of
``radon`` called with ``circle=True``.
Returns
-------
reconstructed : ndarray
Reconstructed image. The rotation axis will be located in the pixel
with indices
``(reconstructed.shape[0] // 2, reconstructed.shape[1] // 2)``.
References
----------
.. [1] AC Kak, M Slaney, "Principles of Computerized Tomographic
Imaging", IEEE Press 1988.
.. [2] B.R. Ramesh, N. Srinivasa, K. Rajgopal, "An Algorithm for Computing
the Discrete Radon Transform With Some Applications", Proceedings of
the Fourth IEEE Region 10 International Conference, TENCON '89, 1989
Notes
-----
It applies the Fourier slice theorem to reconstruct an image by
multiplying the frequency domain of the filter with the FFT of the
projection data. This algorithm is called filtered back projection.
"""
if radon_image.ndim != 2:
raise ValueError('The input image must be 2-D')
if theta is None:
m, n = radon_image.shape
theta = np.linspace(0, 180, n, endpoint=False)
else:
theta = np.asarray(theta)
if len(theta) != radon_image.shape[1]:
raise ValueError("The given ``theta`` does not match the number of "
"projections in ``radon_image``.")
interpolation_types = ('linear', 'nearest', 'cubic')
if interpolation not in interpolation_types:
raise ValueError("Unknown interpolation: %s" % interpolation)
if not output_size:
# If output size not specified, estimate from input radon image
if circle:
output_size = radon_image.shape[0]
else:
output_size = int(
np.floor(np.sqrt((radon_image.shape[0])**2 / 2.0)))
if circle:
radon_image = _sinogram_circle_to_square(radon_image)
th = (np.pi / 180.0) * theta
# resize image to next power of two (but no less than 64) for
# Fourier analysis; speeds up Fourier and lessens artifacts
projection_size_padded = \
max(64, int(2 ** np.ceil(np.log2(2 * radon_image.shape[0]))))
pad_width = ((0, projection_size_padded - radon_image.shape[0]), (0, 0))
img = np.pad(radon_image, pad_width, mode='constant', constant_values=0)
# Construct the Fourier filter
# This computation lessens artifacts and removes a small bias as
# explained in [1], Chap 3. Equation 61
n1 = np.arange(0, projection_size_padded / 2 + 1, dtype=np.int)
n2 = np.arange(projection_size_padded / 2 - 1, 0, -1, dtype=np.int)
n = np.concatenate((n1, n2))
f = np.zeros(projection_size_padded)
f[0] = 0.25
f[1::2] = -1 / (np.pi * n[1::2])**2
# Computing the ramp filter from the fourier transform of is frequency domain representation
# lessens artifacts and removes a small bias as explained in [1], Chap 3. Equation 61
fourier_filter = 2 * np.real(fft(f)) # ramp filter
omega = 2 * np.pi * fftfreq(projection_size_padded)
if filter == "ramp":
pass
elif filter == "shepp-logan":
# Start from first element to avoid divide by zero
fourier_filter[1:] *= np.sin(omega[1:] / 2) / (omega[1:] / 2)
elif filter == "cosine":
freq = (0.5 * np.arange(0, projection_size_padded) /
projection_size_padded)
cosine_filter = np.fft.fftshift(np.sin(2 * np.pi * np.abs(freq)))
fourier_filter *= cosine_filter
elif filter == "hamming":
hamming_filter = np.fft.fftshift(np.hamming(projection_size_padded))
fourier_filter *= hamming_filter
elif filter == "hann":
hanning_filter = np.fft.fftshift(np.hanning(projection_size_padded))
fourier_filter *= hanning_filter
elif filter is None:
fourier_filter[:] = 1
else:
raise ValueError("Unknown filter: %s" % filter)
# Apply filter in Fourier domain
projection = fft(img, axis=0) * fourier_filter[:, np.newaxis]
radon_filtered = np.real(ifft(projection, axis=0))
# Resize filtered image back to original size
radon_filtered = radon_filtered[:radon_image.shape[0], :]
reconstructed = np.zeros((output_size, output_size))
# Determine the center of the projections (= center of sinogram)
mid_index = radon_image.shape[0] // 2
[X, Y] = np.mgrid[0:output_size, 0:output_size]
xpr = X - int(output_size) // 2
ypr = Y - int(output_size) // 2
# Reconstruct image by interpolation
for i in range(len(theta)):
t = ypr * np.cos(th[i]) - xpr * np.sin(th[i])
x = np.arange(radon_filtered.shape[0]) - mid_index
if interpolation == 'linear':
backprojected = np.interp(t,
x,
radon_filtered[:, i],
left=0,
right=0)
else:
interpolant = interp1d(x,
radon_filtered[:, i],
kind=interpolation,
bounds_error=False,
fill_value=0)
backprojected = interpolant(t)
reconstructed += backprojected
if circle:
radius = output_size // 2
reconstruction_circle = (xpr**2 + ypr**2) <= radius**2
reconstructed[~reconstruction_circle] = 0.
return reconstructed * np.pi / (2 * len(th))
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# 時系列のサンプルデータ作成
N = 512 # データ数
dt = 0.01 # サンプリング間隔
f = 20 # 周波数
t = np.linspace(1, N, N) * dt - dt
y = np.sin(2 * np.pi * f * t)
# 離散フーリエ変換
yf = fft(y)
# 周波数スケール作成
# t/dt/dt/N で作成しても良い
freq = fftfreq(N, dt)
# プロット
# 大きさ、位相
plt.figure(1)
plt.subplot(211)
plt.plot(freq[1:N / 2], np.abs(yf)[1:N / 2])
plt.axis('tight')
plt.ylabel("amplitude")
plt.subplot(212)
plt.plot(freq[1:N / 2], np.degrees(np.angle(yf)[1:N / 2]))
plt.axis('tight')
plt.ylim(-180, 180)
plt.xlabel("frequency[Hz]")
plt.ylabel("phase[deg]")
def Traitement_Difference(nom_exp1,
nom_exp2,
nom_resultat,
valeur_resistance,
t1,
t2,
duree,
amplification1=1.,
amplification2=1.,
diviseur=1.,
offset=0.,
freq_coupure=0.):
import numpy as np
from Graphique import Graphique_Simple
from Graphique import Graphique_Double_Echelle
from Integration import Integrale_Trapeze
from Filtre import Passe_bas
from scipy import fftpack
data1 = np.loadtxt(nom_exp1 + '.dat', delimiter=';')
data2 = np.loadtxt(nom_exp2 + '.dat', delimiter=';')
Temps1 = np.asarray(data1[:, 0], dtype=float) / 1000000.
Temps1 = Temps1 - Temps1[0]
Tension1 = (np.asarray(data1[:, 1], dtype=float) -
offset) * diviseur / amplification1
Temps2 = np.asarray(data2[:, 0], dtype=float) / 1000000.
Temps2 = Temps2 - Temps2[0]
Tension2 = (np.asarray(data2[:, 1], dtype=float) -
offset) * diviseur / amplification1
i1 = 0
for i in range(0, Temps1.size):
if abs(Temps1[i1] - t1) > abs(Temps1[i] - t1):
i1 = i
di = 0
for i in range(i1, Temps1.size):
if abs(Temps1[di + i1] - (t1 + duree)) > abs(Temps1[i] - (t1 + duree)):
di = i - i1
i2 = 0
for i in range(0, Temps2.size):
if abs(Temps2[i2] - t2) > abs(Temps2[i] - t2):
i2 = i
Temps = np.zeros(di)
T1 = np.zeros(di)
T2 = np.zeros(di)
for i in range(i1, i1 + di):
Temps[i - i1] = Temps1[i] - Temps1[i1]
T1[i - i1] = Tension1[i]
for i in range(i2, i2 + di):
T2[i - i2] = Tension2[i]
Tension = T1 - T2
freq_echantillonage = Temps[Temps.size - 1] / Temps.size
freqs = fftpack.fftfreq(Temps.size, d=freq_echantillonage)
TFT_M = abs(fftpack.fft(Tension - np.mean(Tension)))
TFT = abs(fftpack.fft(Tension))
Graphique_Simple(Temps,
Tension,
x_label='Temps [s]',
y_label='Tension [V]',
save_name='Graphique_' + nom_resultat + '_T',
graph_name='Difference de la tension au cours du temps')
Graphique_Simple(
freqs,
TFT,
x_label='Temps [s]',
y_label='Tension [V]',
save_name='Graphique_' + nom_resultat + '_TFT',
graph_name='TF Difference de la tension au cours du temps')
Graphique_Simple(
freqs,
TFT_M,
x_label='Temps [s]',
y_label='Tension [V]',
save_name='Graphique_' + nom_resultat + '_TTF-M',
graph_name=
'TF sans la composante continu Difference de la tension au cours du temps'
)
def clean(signals,
confounds=None,
low_pass=0.2,
t_r=2.5,
high_pass=False,
detrend=False,
standardize=True,
shift_confounds=False):
""" Normalize the signal, and if any confounds are given, project in
the orthogonal space.
Low pass filter improves specificity (more interesting arrows
selected)
High pass filter should be kepts small, so as not to kill
sensitivity
"""
if standardize:
signals = _standardize(signals, normalize=True)
elif detrend:
signals = _standardize(signals, normalize=False)
signals = np.asarray(signals)
if confounds is not None:
if isinstance(confounds, basestring):
filename = confounds
confounds = np.genfromtxt(filename)
if np.isnan(confounds.flat[0]):
# There may be a header
if np.version.short_version >= '1.4.0':
confounds = np.genfromtxt(filename, skip_header=1)
else:
confounds = np.genfromtxt(filename, skiprows=1)
# Restrict the signal to the orthogonal of the confounds
confounds = np.atleast_2d(confounds)
if shift_confounds:
confounds = np.r_[confounds[..., 1:-1], confounds[..., 2:],
confounds[..., :-2]]
signals = signals[..., 1:-1]
confounds = _standardize(confounds, normalize=True)
confounds = qr_economic(confounds)[0].T
signals -= np.dot(np.dot(signals, confounds.T), confounds)
if low_pass and high_pass and high_pass >= low_pass:
raise ValueError("Your value for high pass filter (%f) is higher or"
" equal to the value for low pass filter (%f). This"
" would result in a blank signal" %
(high_pass, low_pass))
if low_pass or high_pass:
n = signals.shape[-1]
freq = fftpack.fftfreq(n, d=t_r)
for s in signals:
fft = fftpack.fft(s)
if low_pass:
fft[np.abs(freq) > low_pass] = 0
if high_pass:
fft[np.abs(freq) < high_pass] = 0
s[:] = fftpack.ifft(fft)
if detrend:
# This is faster than scipy.detrend and equivalent
regressor = np.arange(signals.shape[1]).astype(np.float)
regressor -= regressor.mean()
regressor /= np.sqrt((regressor**2).sum())
signals -= np.dot(signals, regressor)[:, np.newaxis] * regressor
if standardize:
signals = _standardize(signals, normalize=True)
elif detrend:
signals = _standardize(signals, normalize=False)
return signals
import numpy as np
import matplotlib.pyplot as plt
import math
import scipy.fftpack as syfp
x = np.linspace(0, 5, 1000)
hanning = np.hanning(len(x))
y = np.sin(2 * math.pi * x)
plt.plot(x, y)
plt.show()
fft = np.fft.fft(x)
fft_freq = np.fft.fftfreq(len(x), x[1] - x[0])
freqs = syfp.fftfreq(len(x), x[1] - x[0])
plt.semilogy(freqs, abs(fft))
plt.axvline(1, color="red", linestyle="--")
plt.show()
import scipy as sy
import scipy.fftpack as syfp
dt = 0.02071
t = np.linspace(0, 10, 1000) ## time at the same spacing of your data
freq = 10
u = np.sin(2 * np.pi * t * freq) ## Note freq=0.01 Hz
# Do FFT analysis of array
FFT = sy.fft.fft(u)
# Getting the related frequencies
freqs = syfp.fftfreq(len(u), t[1] -
t[0]) ## added dt, so x-axis is in meaningful units
import numpy as np
import matplotlib.pyplot as plt
from scipy.fftpack import fft, fftfreq
datos = np.genfromtxt("funcion.dat")
t = datos[:, 0]
f = datos[:, 1]
def fourier(function):
N = len(function)
fourier = np.zeros(N)
for i in range(N):
coeficientes = 0.0
for j in range(N):
coeficientes += function[j] * np.exp((-2 * np.pi * 1j * i * j) / N)
fourier[i] = abs(coeficientes)
return fourier
n = len(f)
x = fourier(f) / n
dt = t[2] - t[1]
freq = fftfreq(n, dt)
fmax = np.argmax(x)
frecuencia = int(freq[fmax])
print('La frecuencia es:', frecuencia, 'Hz')
def iterate(self, iloop, save_wisdom=1):
dat = self.dat
ran = self.ran
smooth = self.smooth
binsize = self.binsize
beta = self.beta
bias = self.bias
f = self.f
nbins = self.nbins
#-- Creating arrays for FFTW
if iloop == 0:
delta = pyfftw.empty_aligned((nbins, nbins, nbins),
dtype='complex128')
deltak = pyfftw.empty_aligned((nbins, nbins, nbins),
dtype='complex128')
psi_x = pyfftw.empty_aligned((nbins, nbins, nbins),
dtype='complex128')
psi_y = pyfftw.empty_aligned((nbins, nbins, nbins),
dtype='complex128')
psi_z = pyfftw.empty_aligned((nbins, nbins, nbins),
dtype='complex128')
#delta = np.zeros((nbins, nbins, nbins), dtype='complex128')
#deltak= np.zeros((nbins, nbins, nbins), dtype='complex128')
#psi_x = np.zeros((nbins, nbins, nbins), dtype='complex128')
#psi_y = np.zeros((nbins, nbins, nbins), dtype='complex128')
#psi_z = np.zeros((nbins, nbins, nbins), dtype='complex128')
print 'Allocating randoms in cells...'
deltar = self.allocate_gal_cic(ran)
print 'Smoothing...'
deltar = gaussian_filter(deltar, smooth / binsize)
#-- Initialize FFT objects and load wisdom if available
wisdomFile = "wisdom." + str(nbins) + "." + str(self.nthreads)
if os.path.isfile(wisdomFile):
print 'Reading wisdom from ', wisdomFile
g = open(wisdomFile, 'r')
wisd = json.load(g)
pyfftw.import_wisdom(wisd)
g.close()
print 'Creating FFTW objects...'
fft_obj = pyfftw.FFTW(delta, delta, axes=[0, 1, 2], \
threads=self.nthreads)
ifft_obj = pyfftw.FFTW(deltak, psi_x, axes=[0, 1, 2], \
threads=self.nthreads, \
direction='FFTW_BACKWARD')
else:
delta = self.delta
deltak = self.deltak
deltar = self.deltar
psi_x = self.psi_x
psi_y = self.psi_y
psi_z = self.psi_z
fft_obj = self.fft_obj
ifft_obj = self.ifft_obj
#fft_obj = pyfftw.FFTW(delta, delta, threads=self.nthreads, axes=[0, 1, 2])
#-- Allocate galaxies and randoms to grid with CIC method
#-- using new positions
print 'Allocating galaxies in cells...'
deltag = self.allocate_gal_cic(dat)
print 'Smoothing...'
deltag = gaussian_filter(deltag, smooth / binsize)
print 'Computing fluctuations...'
delta[:] = deltag - self.alpha * deltar
w = np.where(deltar > self.ran_min)
delta[w] = delta[w] / (self.alpha * deltar[w])
w2 = np.where((deltar <= self.ran_min))
delta[w2] = 0.
#-- removing this to not change statistics
#w3=np.where(delta>np.percentile(delta[w].ravel(), 99))
#delta[w3] = 0.
del (w)
del (w2)
#del(w3)
del (deltag)
print 'Fourier transforming delta field...'
norm_fft = 1. #binsize**3
fft_obj(input_array=delta, output_array=delta)
#delta = pyfftw.builders.fftn(\
# delta, axes=[0, 1, 2], \
# threads=self.nthreads, overwrite_input=True)()
#-- delta/k**2
k = fftfreq(self.nbins, d=binsize) * 2 * np.pi
#-- adding 1e-100 in order to avoid division by zero
delta /= (k[:, None, None]**2 + k[None, :, None]**2 +
k[None, None, :]**2 + 1e-100)
delta[0, 0, 0] = 0.
#-- Estimating the IFFT in Eq. 12 of Burden et al. 2015
print 'Inverse Fourier transforming to get psi...'
norm_ifft = 1. #(k[1]-k[0])**3/(2*np.pi)**3*nbins**3
deltak[:] = delta * -1j * k[:, None, None] / bias
ifft_obj(input_array=deltak, output_array=psi_x)
deltak[:] = delta * -1j * k[None, :, None] / bias
ifft_obj(input_array=deltak, output_array=psi_y)
deltak[:] = delta * -1j * k[None, None, :] / bias
ifft_obj(input_array=deltak, output_array=psi_z)
#psi_x = pyfftw.builders.ifftn(\
# delta*-1j*k[:, None, None]/bias, \
# axes=[0, 1, 2], \
# threads=self.nthreads, overwrite_input=True)().real
#psi_y = pyfftw.builders.ifftn(\
# delta*-1j*k[None, :, None]/bias, \
# axes=[0, 1, 2], \
# threads=self.nthreads, overwrite_input=True)().real
#psi_z = pyfftw.builders.ifftn(\
# delta*-1j*k[None, None, :]/bias, \
# axes=[0, 1, 2], \
# threads=self.nthreads, overwrite_input=True)().real
#psi_x = ifftn(-1j*delta*k[:, None, None]/bias).real*norm_ifft
#psi_y = ifftn(-1j*delta*k[None, :, None]/bias).real*norm_ifft
#psi_z = ifftn(-1j*delta*k[None, None, :]/bias).real*norm_ifft
#-- removing RSD from galaxies
shift_x, shift_y, shift_z = \
self.get_shift(dat, psi_x.real, psi_y.real, psi_z.real, \
use_newpos=True)
print "Few displacement values: "
for i in range(10):
print shift_x[i], shift_y[i], shift_z[i], dat.x[i]
#-- for first loop need to approximately remove RSD component
#-- from Psi to speed up calculation
#-- first loop so want this on original positions (cp),
#-- not final ones (np) - doesn't actualy matter
if iloop == 0:
psi_dot_rhat = (shift_x*dat.x + \
shift_y*dat.y + \
shift_z*dat.z ) /dat.dist
shift_x -= beta / (1 + beta) * psi_dot_rhat * dat.x / dat.dist
shift_y -= beta / (1 + beta) * psi_dot_rhat * dat.y / dat.dist
shift_z -= beta / (1 + beta) * psi_dot_rhat * dat.z / dat.dist
#-- remove RSD from original positions (cp) of
#-- galaxies to give new positions (np)
#-- these positions are then used in next determination of Psi,
#-- assumed to not have RSD.
#-- the iterative procued then uses the new positions as
#-- if they'd been read in from the start
psi_dot_rhat = (shift_x * dat.x + shift_y * dat.y +
shift_z * dat.z) / dat.dist
dat.newx = dat.x + f * psi_dot_rhat * dat.x / dat.dist
dat.newy = dat.y + f * psi_dot_rhat * dat.y / dat.dist
dat.newz = dat.z + f * psi_dot_rhat * dat.z / dat.dist
self.deltar = deltar
self.delta = delta
self.deltak = deltak
self.psi_x = psi_x
self.psi_y = psi_y
self.psi_z = psi_z
self.fft_obj = fft_obj
self.ifft_obj = ifft_obj
#-- save wisdom
wisdomFile = "wisdom." + str(nbins) + "." + str(self.nthreads)
if iloop == 0 and save_wisdom and not os.path.isfile(wisdomFile):
wisd = pyfftw.export_wisdom()
f = open(wisdomFile, 'w')
json.dump(wisd, f)
f.close()
print 'Wisdom saved at', wisdomFile
else:
return_value = new_data, new_coord
return return_value
def padded(to_pad, max_len):
length = len(to_pad)
zeros = max_len - length
to_pad = list(to_pad)
for i in range(zeros):
to_pad.append(0)
return to_pad
# In[3]:
zonal_spacing = fftfreq(240, 1.5)
zonal_spacing = 1 / zonal_spacing
zonal_spacing = 360 / zonal_spacing
# In[4]:
# get file neams for detrending
from os import walk
f = []
for (dirpath, dirnames, filenames) in walk('gphfiles/'):
f.extend(filenames)
break
for wantfile in range(len(f)):
nco_sine = np.sin(2 * np.pi * nco_freq * t)
i_post_mix = adc_out * nco_cosine
q_post_mix = adc_out * nco_sine
# using cusomized fft module
x, y = fftplot.winfft(i_post_mix, fs=fs)
plt.figure()
fftplot.plot_spectrum(x, y)
plt.title(f'Output Spectrum of i_post_mix - {ftone / 1e6} MHz Tone')
# using cusomized fft module
x, y = fftplot.winfft(q_post_mix, fs=fs)
plt.figure()
fftplot.plot_spectrum(x, y)
plt.title(f'Output Spectrum of q_post_mix - {ftone / 1e6} MHz Tone')
plt.figure()
yf = fft.fft(adc_out)
xf = fft.fftfreq(nsamps, 1 / fs)
xf = fft.fftshift(xf)
yf = fft.fftshift(yf)
plt.plot(xf / 1e3, np.abs(yf))
plt.figure()
plt.stem(xf / 1e3,
angle2(np.round(yf, 1)) * 180 / pi,
use_line_collection=True)
plt.show()
def spec_plot(title=0,
data=d2_averages[0],
levels="no",
save=False,
name=None):
#select a season for plotting
test_dat = data
frequencies = fftfreq(len(test_dat[1]), 0.25)
#set what you wanna crop
max_z = 40
max_f = 1
#crop the data, only keep the positive frequencies
cropped = [[
test_dat[i][j] for i in range(len(zonal_spacing))
if zonal_spacing[i] <= max_z and zonal_spacing[i] >= 0
] for j in range(len(frequencies)) if np.abs(frequencies[j]) <= max_f]
cropf = [
counted for counted in frequencies if np.abs(counted) <= max_f
] # and counted != 0]
cropz = [
zonal_spacing[i] for i in range(len(zonal_spacing))
if zonal_spacing[i] <= max_z and zonal_spacing[i] >= 0
]
x = cropf
y = cropz
X, Y = np.meshgrid(x, y)
X = np.flip(X, 1)
Z = np.transpose(np.abs(cropped))
# add cyclic point for plotting purposes
x = np.array(x)
testZ = [fftshift(entry) for entry in Z]
testZ = np.array(testZ)
dataout, lonsout = add_cyclic_point(testZ, fftshift(x))
x = lonsout
y = y
X, Y = np.meshgrid(x, y)
X = np.flip(X, 1)
# set colors and levels for discrete values
# colors_set = cubehelix_palette(10)
colors_set = sns.cubehelix_palette(10,
start=2,
rot=0,
dark=0,
light=.95)
if levels == "no":
# set colors and levels for discrete values
level_set_less = [
np.percentile(dataout, j * 10) for j in range(1, 11)
]
for j in range(1, 5):
level_set_less.append(np.percentile(dataout, 90 + 2 * j))
#level_set_less = flatten(level_set_less)
level_set_less.sort()
levels_rec.append(level_set_less)
else:
level_set_less = levels
colors_set = sns.palplot(sns.color_palette("hls", len(level_set_less)))
colors_set = sns.cubehelix_palette(14,
start=2,
rot=0,
dark=0,
light=.95)
colors_set = sns.color_palette("cubehelix", 14)
# plot it
plt.clf()
plt.figure(figsize=(15, 5), constrained_layout=True)
# actual plot
CF = plt.contourf(
X,
Y,
dataout,
colors=colors_set,
levels=level_set_less,
)
# set colorbars
CBI = plt.colorbar(CF)
ax = CBI.ax
ax.text(-2.5, 0.8, 'Coefficient magnitude', rotation=90)
# ax.yaxis.get_offset_text().set_position((-3, 5))
labels = ["{:.1E}".format(Decimal(entry)) for entry in level_set_less]
CBI.set_ticklabels(labels)
# plot labels
plt.xlabel(r"Frequency (day$^{-1}$)")
plt.ylim(ymax=25, ymin=3)
plt.xlim(xmax=0.75, xmin=-0.75)
plt.ylabel("Zonal wavenumber")
plt.title(str(title) + " climatology of geopotential height spectra",
pad=15)
# formatting
sns.set_style("ticks")
sns.set_context("poster")
sns.despine()
if save == True:
plt.savefig(name, bbox_inches="tight")
# PROCEDIMIENTO
dt=(tn-t0)/n # intervalo de muestreo
# Analógica Referencia para mostrar que es par
fs=20
t=np.arange(-tn,tn,dt) # eje tiempo analógica
m=len(t)
xanalog=np.zeros(m, dtype=float)
for i in range(0,m):
xanalog[i]=entradax(t[i],fs)
# FFT: Transformada Rapida de Fourier
# Analiza la parte t>=0 de xnalog muestras[n:2*n]
xf=fourier.fft(xanalog[n:2*n])
xf=fourier.fftshift(xf)
# Rango de frecuencia para eje
frq=fourier.fftfreq(n, dt)
frq=fourier.fftshift(frq)
# x[w] real
xfreal=(1/n)*np.real(xf)
# x[w] imaginario
xfimag=(1/n)*np.imag(xf)
# x[w] magnitud
xfabs=(1/n)*np.abs(xf)
# x[w] angulo
xfangle=(1/n)*np.unwrap(np.angle(xf))
#SALIDA
plt.figure(1) # define la grafica
plt.suptitle('Transformada Rápida Fourier FFT')
x0 = int(x_length / 2) # Constants hbar = 1 m = 1 omega = 0.01 sigma = np.sqrt(hbar / (2 * m * omega)) # Defining Wavefunction psi = wave_init(x, sigma, x0-50) V_x = harmonic_potential(x, m, omega, x0) #V_x = np.zeros(N) # Defining k dk = dx / (2 * np.pi) k = fftfreq(N, dk) ks = fftshift(k) # Defining time steps t = 0 dt = 5 step = 1 sch = Schrodinger(x, psi, V_x, k, hbar, m, t) print(sch.norm_x()) x_limits = ((x[0],x[N-1]), (0, 0.16)) k_limits = ((-5, 5), (0, max(abs(sch.psi_k)+0.5)))
def k_z(self):
f_z = fftpack.fftshift(fftpack.fftfreq(self.Nz, d=self.d_z))
k_z = 2 * np.pi * f_z
return k_z
# ---------------
# Grid properties
# ---------------
c_cm_ps = c * 1e2 / 1e12
c_nm_ps = c * 1e9 / 1e12
num_bits = 12
num_grid_points = 2**num_bits # use powers of 2 for efficient FFT's
time_window_width = 50 # [ps]
tms = sp.linspace(-time_window_width / 2, time_window_width / 2,
num_grid_points)
wavelength_signal = 1040.0 # [nm]
wavelength_pump = 976.0 # [nm]
num_points = len(tms) # number of grid points
dt = tms[1] - tms[0] # time spacing [ps]
freqs = fftshift(fftfreq(num_points, dt)) # [THz]
omegas_centered_on_zero = (2 *
sp.pi) * freqs # angular frequency about zero
omega_centre_signal = (
2 * sp.pi *
c_nm_ps) / wavelength_signal # angular reference frequency [TCycles]
omega_centre_pump = (
2 * sp.pi *
c_nm_ps) / wavelength_pump # angular reference frequency [TCycles]
omegas = omegas_centered_on_zero + omega_centre_signal
omegas_pump = omegas_centered_on_zero + omega_centre_pump
wls = 2 * sp.pi * c_nm_ps / omegas # wavelength grid [nm] - need a wls grid for the signal centered at 1040 nm
wls_pump = 2 * sp.pi * c_nm_ps / omegas_pump # wavelength grid [nm]- need a wls grid for the pump centered at 976 nm
# -----------
# Man kan gemme reference til de enkelte lyde (lyd objekter) og starte/stoppe dem individuelt... Eksperimenter med det i senere udgave
# Man hører kun de første 8 lyde i sweep når man sætter konstanten til True ;-) Så det er ikke så fedt.... Så bør man justere de andre
# konstanter til sådan at man kun kommer rundt i loop 8 gange...
#
sound = pygame.sndarray.make_sound(signal)
sound.play(-1)
#
# Hvis konstanten PLOT er True så fylder vi figuren med plot af den lyd som spiller
#
if PLOT:
left_curve, = left_plot.plot(time, signal.T[0])
right_curve, = right_plot.plot(time, signal.T[1])
combined = signal.T[0] + signal.T[1]
combined_curve, = combined_plot.plot(time, combined)
FFT = abs(fft(combined))
freqs = fftfreq(combined.size, 1 / SAMPLERATE)
fft_curve, = fft_plot.plot(freqs, np.log10(FFT))
#
# Aht at få tegnet plot færdigt inden en pause bruges plt.pause hvis vi laver plot ellers pygame delay
#
if PLOT: plt.pause(DURATION - 0.1)
else: pygame.time.delay(500)
#
# Med konstanterne kan man styre om der kun tegnes een kurve for den lyd der spiller eller om de tegnes oveni hinanden.
# Nedenfor slettes gamle kurver hvis ONLY_ONE_CURVE er True. FFT får særstatus og kan styres individuelt.
#
if PLOT and ONLY_ONE_CURVE:
left_plot.lines.remove(left_curve)
right_plot.lines.remove(right_curve)
combined_plot.lines.remove(combined_curve)
plt.xlabel("z (kpc)")
plt.ylabel("W(z,theta)")
plt.legend()
plt.savefig("../images/Figure 7.png", dpi=400)
plt.show()
ws = np.zeros((2000, 4000))
ft_ws = np.zeros((2000, 4000))
freqs_ws = np.zeros((2000, 4000))
i = 0
for theta in range(0, 2000, 1):
ws[i, :] = windowFunc(theta, zs)
ft_ws[i, :] = np.abs(fftpack.fft(
ws[i, :]))**2 #square of partial FT (wrt) of window function
freqs_ws[i, :] = fftpack.fftfreq(len(ws[i, :]), d=(zs[1] - zs[0]))
i += 1
plt.figure()
plt.imshow(ws)
plt.xlabel("z (-2000 to 2000 kpc)")
plt.ylabel("theta (0-2000 kpc)")
plt.title(r"$W(z,\theta)$")
plt.savefig("../images/Window Function.png", dpi=400)
plt.colorbar()
plt.show()
plt.figure()
plt.plot(freqs_ws[0, :], ft_ws[0, :], label="theta=0 kpc")
plt.plot(freqs_ws[500, :], ft_ws[500, :], label="theta=500 kpc")
plt.loglog()