def test_definition(self):
for n in [16,17,64,127]:
x = arange(n)*2*pi/n
y = ihilbert(sin(x))
y1 = direct_ihilbert(sin(x))
assert_array_almost_equal(y,y1)
assert_array_almost_equal(ihilbert(sin(2*x)),
direct_ihilbert(sin(2*x)))
def test_random_odd(self):
for n in [33,65,55]:
f = random((n,))
af = sum(f,axis=0)/n
f = f-af
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(ihilbert(hilbert(f)),f)
assert_array_almost_equal(hilbert(ihilbert(f)),f)
def calc_edge(numpeaks, ene, pdos):
import numpy as np
from scipy import fftpack
#
# take upper edge by inverse Hilbert transform
#
ih = fftpack.ihilbert(pdos)
ihpeaks = findpeak(ene, abs(ih))
upper_edge = np.zeros(numpeaks)
lower_edge = np.zeros(numpeaks)
for peak in ihpeaks:
if ih[peak] > 0.0 and ih[peak] > 0.8 * max(
ih): # just choose large peak, positive part
upper_edge = np.insert(upper_edge, 0, ene[peak])
elif ih[peak] <= 0.0 and ih[peak] < 0.8 * min(ih):
lower_edge = np.insert(lower_edge, 0, ene[peak])
upper_edge = upper_edge[0:numpeaks]
lower_edge = lower_edge[0:numpeaks]
#upper_edge = upper_edge[::-1]
#lower_edge = lower_edge[::-1]
return upper_edge, lower_edge
def test_itilbert_relation(self):
for n in [16,17,64,127]:
x = arange(n)*2*pi/n
f = sin(x)+cos(2*x)*sin(x)
y = ihilbert(f)
y1 = direct_ihilbert(f)
assert_array_almost_equal(y,y1)
y2 = itilbert(f,h=10)
assert_array_almost_equal(y,y2)
def test_random_even(self):
for n in [32,64,56]:
f = random((n,))
af = sum(f,axis=0)/n
f = f-af
# zeroing Nyquist mode:
f = diff(diff(f,1),-1)
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(direct_hilbert(direct_ihilbert(f)),f)
assert_array_almost_equal(hilbert(ihilbert(f)),f)
def compute_group_vel(ccf_full, ccf, t_ccf, dist, tmin, tmax, vmin, vmax,
alpha):
#构建中心周期序列
#per=np.arange(tmin,tmax+0.1,0.1)
delta = 0.1
per = []
cper = tmin
while cper < tmax:
per.append(cper)
cper += delta
delta *= 1.01
if per[-1] < tmax: per.append(tmax)
#将 ccf 变换到频率域
ccf_freq = fftpack.ifft(ccf)
freq_samp = 2 * np.pi * abs(fftpack.fftfreq(len(ccf)))
ccf_full_freq = fftpack.ifft(ccf_full)
freq_full_samp = 2 * np.pi * abs(fftpack.fftfreq(len(ccf_full)))
#时频分析
SSNR = []
t_ariv = []
ph_ariv = []
per_inst = []
omg_inst = []
group_vel = []
ftan_mat = []
for tn in per:
omgn = 2 * np.pi / tn
#窄带滤波
ccf_freq_nbG=ccf_freq*np.exp(-alpha*((freq_samp-omgn)\
/omgn)**2)
ccf_full_freq_nbG=ccf_full_freq*\
np.exp(-alpha*((freq_full_samp-omgn)/omgn)**2)
#变换到时间域
ccf_time_nbG = fftpack.fft(ccf_freq_nbG).real
ccf_full_time_nbG = fftpack.fft(ccf_full_freq_nbG).real
ccf_time_nbG_hilbert = fftpack.ihilbert(ccf_time_nbG)
#计算包络
env = np.sqrt(ccf_time_nbG**2 + ccf_time_nbG_hilbert**2)
#amp=20*np.log10(env) #单位:DB
amp = env.copy()
[env, t_env] = bspline_itp(env, t_ccf)
#计算相位
phase = np.arctan(ccf_time_nbG_hilbert / ccf_time_nbG)
for i in range(len(phase) - 1):
k = int(abs(phase[i + 1] - phase[i]) / np.pi + 1 / 2)
phase[i + 1] = phase[i + 1] + np.pi * k
[phase, t_phase] = linear_itp(phase, t_ccf)
#计算瞬时频率
index = np.where(env == np.max(env))[0][0]
try:
omgn = (phase[index + 1] - phase[index]) / (t_phase[index + 1] -
t_phase[index])
except:
continue
if omgn < 0:
continue
omg_inst.append(omgn)
t_ariv.append(t_env[index])
while phase[index] > np.pi / 2:
phase[index] = phase[index] - np.pi
ph_ariv.append(phase[index])
#计算群速度
per_inst.append(float(str(round(2 * np.pi / omg_inst[-1], 3))))
group_vel.append(dist / t_ariv[-1])
ftan_mat.append(list(amp))
#计算谱信噪比
index1 = int(dist / vmax)
index2 = int(dist / vmin)
signal = ccf_full_time_nbG[index1:index2 + 1]
noise = ccf_full_time_nbG[index1 + 1000:index2 + 1001]
noise_rms = np.sqrt(np.sum(noise**2) / len(noise))
SSNR.append(np.max(signal) / noise_rms)
#print(tn,2*np.pi/omgn)
#plt.subplot(211)
#plt.plot(t_ccf,ccf,'k')
#plt.subplot(212)
#plt.plot(amp,'k')
#plt.show()
ftan_mat = np.transpose(ftan_mat)
ftan_mat = 100 * ftan_mat / np.max(ftan_mat)
#调整振幅(开方乘十),为了画图好看
tmp = []
for line in ftan_mat:
tmp.append(np.sqrt(np.sqrt(line) * 10) * 10)
ftan_mat = tmp.copy()
#plt.plot(per_inst,SSNR)
#plt.show()
return (ftan_mat, group_vel, per_inst, omg_inst, t_ariv, ph_ariv, SSNR)
height_vir.append(peak[1])
width_vir.append(peak[2])
area_vir.append(peak[1] * peak[2] * np.sqrt(np.pi))
#
# if you want to check by eye
#
if check:
import matplotlib.pylab as plt
import seaborn as sb
from scipy import fftpack
#print("upper edge:{}".format(upper_edge))
#print("lower edge:{}".format(lower_edge))
fit = fit_func(ene, *params)
ih = fftpack.ihilbert(pdos)
sb.set(context='notebook',
style='darkgrid',
palette='deep',
font='sans-serif',
font_scale=1,
color_codes=False,
rc=None)
plt.plot(ene, fit, label="fitted")
plt.plot(ene, pdos, label="original")
plt.vlines(position_occ,
0,
np.max(pdos),
linestyle="dashed",
linewidth=0.5)