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202 | #!/usr/bin/env python
# -*- coding: utf-8 -*-
from matplotlib.pyplot import *
from numpy import *
#from scipy.fftpack import rfft, irfft,fftshift,ifft
from numpy.fft import rfft, irfft,fftshift,ifft
from _extend import extend
import sys
from scipy import signal
"""
Continuous Multi-Wavelet analyzis 0.1
Description:
The continius wavelet analysis od the multiple signal is calculated. Instead
of the single one dimensional wavelet a n-dimensional Morlet wavelet with shifted component is created.
The moving scalar product with such wavelets helps to identify and amplify the correctly time shifted
signals and suppress the other.
"""
__all__ = ["NTM_CWT", "angularfreq", "scales", "compute_s0"]
def angularfreq(N, dt):
"""Compute angular frequencies.
:Parameters:
N : integer
number of data samples
dt : float
time step
:Returns:
angular frequencies : 1d numpy array
"""
# See (5) at page 64.
N2 = N / 2.0
w = empty(N)
for i in range(w.shape[0]):
if i <= N2:
w[i] = (2 * pi * i) / (N * dt)
else:
w[i] = (2 * pi * (i - N)) / (N * dt)
return w
def scales(N, dj, dt, s0):
"""Compute scales.
:Parameters:
N : integer
number of data samples
dj : float
scale resolution
dt : float
time step
:Returns:
scales : 1d numpy array
scales
"""
# See (9) and (10) at page 67.
J = floor(dj**-1 * log2((N * dt) / s0))
s = empty(J + 1)
for i in range(s.shape[0]):
s[i] = s0 * 2**(i * dj)
return s
def compute_s0(dt, p):
"""Compute s0.
:Parameters:
dt :float
time step
p : float
omega0 ('morlet') or order ('paul', 'dog')
:Returns:
s0 : float
"""
return (dt * (p + sqrt(2 + p**2))) / (2 * pi)
def NTM_CWT((x, dt, dj, p,m , res, fmin,fmax)):
n_detec = size(x,1)
lenght = size(x,0)
lenght_ext = int(2**ceil(log2(lenght)))
x = signal.detrend(x, axis=0, type='linear')
x_new = extend(x, method='zeros')
w = angularfreq(lenght_ext, dt)
s0 = compute_s0(dt, p)
s = scales(lenght_ext, dj, dt, s0)
freq = (p + sqrt(2.0 + p**2))/(4*pi * s)
ind = where((freq>fmin)&(freq<fmax))
s = s[ind]
x = rfft(x_new, axis=0)
x[::2]*= -1 #magic :-)
step = max(int(lenght_ext/res),1)
stmp = zeros(1)
faze = arange(n_detec)/double(n_detec)*m
faze = matrix(faze)
wft = zeros((len(w)),dtype=cfloat )
exp_phase = exp(-2*pi*1j*faze)
f_max = 1/dt
spec = list()
for i in range(len(s)):
#sys.stdout.write('\r %.1f%%'%(i*100./(len(s))))
#sys.stdout.flush()
interv = (((abs(s[i]*w[:len(w)/2]-p)) < 5))
arg = s[i]*w[interv]-p
arg += 1e-2/(1-w[interv]/w[len(w)/2]+0.001)
wavelet= (1+sign(w[interv]))*exp(-(arg )**2/2)*sqrt(abs(s[i])/dt)
#tady by Å¡lo udÄlat aby pro každou frekvenci bylo jiné okno
wavelet = matrix(wavelet, copy = False)
wft[interv] = sum(multiply(x[interv],wavelet.T*exp_phase),1)
wft = ifft(wft)
spec.append(fftshift(wft[::step]))
wft[:] = 0
spec = array(spec, copy = False)
spec/= n_detec
n_edge = (lenght_ext/float(lenght)-1)*size(spec,1)/2
spec = spec[:,int(n_edge):-int(n_edge)]
s*=max(abs(m),1)
return spec, s
|
