N = 1024
t = np.linspace(-5, 5, N)
x = np.ones(len(t))
h = np.random.normal(0, 1, len(t))
h *= np.exp(-0.5 * (t / 0.5) ** 2)
#------------------------------------------------------------
# Compute an example wavelet
W = sinegauss(t, 0, 1.5, Q=1.0)
#------------------------------------------------------------
# Compute the wavelet PSD
f0 = np.linspace(0.5, 7.5, 100)
wPSD = wavelet_PSD(t, h, f0, Q=1.0)
#------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(8, 8))
fig.subplots_adjust(hspace=0.05, left=0.12, right=0.95, bottom=0.08, top=0.95)
# First panel: the signal
ax = fig.add_subplot(311)
ax.plot(t, h, '-k', lw=1)
ax.text(0.02, 0.95, ("Input Signal:\n"
"Localized Gaussian noise"),
ha='left', va='top', transform=ax.transAxes)
ax.set_xlim(-4, 4)
ax.set_ylim(-2.9, 2.9)
N = 1024
t = np.linspace(-5, 5, N)
x = np.ones(len(t))
h = np.random.normal(0, 1, len(t))
h *= np.exp(-0.5 * (t / 0.5)**2)
#------------------------------------------------------------
# Compute an example wavelet
W = sinegauss(t, 0, 1.5, Q=1.0)
#------------------------------------------------------------
# Compute the wavelet PSD
f0 = np.linspace(0.5, 7.5, 100)
wPSD = wavelet_PSD(t, h, f0, Q=1.0)
#------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(5, 5))
fig.subplots_adjust(hspace=0.05, left=0.12, right=0.95, bottom=0.08, top=0.95)
# First panel: the signal
ax = fig.add_subplot(311)
ax.plot(t, h, '-k', lw=1)
ax.text(0.02,
0.95, ("Input Signal:\n"
"Localized Gaussian noise"),
ha='left',
va='top',
transform=ax.transAxes)
def compute_Gaussian():
from astroML.fourier import\
FT_continuous, IFT_continuous, sinegauss, sinegauss_FT, wavelet_PSD
#----------------------------------------------------------------------
# This function adjusts matplotlib settings for a uniform feel in the textbook.
# Note that with usetex=True, fonts are rendered with LaTeX. This may
# result in an error if LaTeX is not installed on your system. In that case,
# you can set usetex to False.
from astroML.plotting import setup_text_plots
setup_text_plots(fontsize=8, usetex=False)
#------------------------------------------------------------
# Sample the function: localized noise
np.random.seed(0)
N = 1024
t = np.linspace(-5, 5, N)
x = np.ones(len(t))
h = np.random.normal(0, 1, len(t))
h *= np.exp(-0.5 * (t / 0.5) ** 2)
#------------------------------------------------------------
# Compute an example wavelet
W = sinegauss(t, 0, 1.5, Q=1.0)
#------------------------------------------------------------
# Compute the wavelet PSD
f0 = np.linspace(0.5, 7.5, 100)
wPSD = wavelet_PSD(t, h, f0, Q=1.0)
#------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(5, 5))
fig.subplots_adjust(hspace=0.05, left=0.12, right=0.95, bottom=0.08, top=0.95)
# First panel: the signal
ax = fig.add_subplot(311)
ax.plot(t, h, '-k', lw=1)
ax.text(0.02, 0.95, ("Input Signal:\n"
"Localized Gaussian noise"),
ha='left', va='top', transform=ax.transAxes)
ax.set_xlim(-4, 4)
ax.set_ylim(-2.9, 2.9)
ax.xaxis.set_major_formatter(plt.NullFormatter())
ax.set_ylabel('$h(t)$')
# Second panel: an example wavelet
ax = fig.add_subplot(312)
ax.plot(t, W.real, '-k', label='real part', lw=1)
ax.plot(t, W.imag, '--k', label='imag part', lw=1)
ax.text(0.02, 0.95, ("Example Wavelet\n"
"$t_0 = 0$, $f_0=1.5$, $Q=1.0$"),
ha='left', va='top', transform=ax.transAxes)
ax.text(0.98, 0.05,
(r"$w(t; t_0, f_0, Q) = e^{-[f_0 (t - t_0) / Q]^2}"
"e^{2 \pi i f_0 (t - t_0)}$"),
ha='right', va='bottom', transform=ax.transAxes)
ax.legend(loc=1)
ax.set_xlim(-4, 4)
ax.set_ylim(-1.4, 1.4)
ax.set_ylabel('$w(t; t_0, f_0, Q)$')
ax.xaxis.set_major_formatter(plt.NullFormatter())
# Third panel: the spectrogram
ax = plt.subplot(313)
ax.imshow(wPSD, origin='lower', aspect='auto', cmap=plt.cm.jet,
extent=[t[0], t[-1], f0[0], f0[-1]])
ax.text(0.02, 0.95, ("Wavelet PSD"), color='w',
ha='left', va='top', transform=ax.transAxes)
ax.set_xlim(-4, 4)
ax.set_ylim(0.5, 7.5)
ax.set_xlabel('$t$')
ax.set_ylabel('$f_0$')
plt.show()
def compute_Chirp():
from astroML.fourier import FT_continuous, IFT_continuous, wavelet_PSD
#----------------------------------------------------------------------
# This function adjusts matplotlib settings for a uniform feel in the textbook.
# Note that with usetex=True, fonts are rendered with LaTeX. This may
# result in an error if LaTeX is not installed on your system. In that case,
# you can set usetex to False.
from astroML.plotting import setup_text_plots
setup_text_plots(fontsize=8, usetex=False)
#------------------------------------------------------------
# Define the chirp signal
def chirp(t, T, A, phi, omega, beta):
signal = A * np.sin(phi + omega * (t - T) + beta * (t - T) ** 2)
signal[t < T] = 0
return signal
def background(t, b0, b1, Omega1, Omega2):
return b0 + b1 * np.sin(Omega1 * t) * np.sin(Omega2 * t)
N = 4096
t = np.linspace(-50, 50, N)
h_true = chirp(t, -20, 0.8, 0, 0.2, 0.02)
h = h_true + np.random.normal(0, 1, N)
#------------------------------------------------------------
# Compute the wavelet PSD
f0 = np.linspace(0.04, 0.6, 100)
wPSD = wavelet_PSD(t, h, f0, Q=1.0)
#------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(5, 3.75))
fig.subplots_adjust(hspace=0.05, left=0.1, right=0.95, bottom=0.1, top=0.95)
# Top: plot the data
ax = fig.add_subplot(211)
ax.plot(t + 50, h, '-', c='#AAAAAA')
ax.plot(t + 50, h_true, '-k')
ax.text(0.02, 0.95, "Input Signal: chirp",
ha='left', va='top', transform=ax.transAxes,
bbox=dict(boxstyle='round', fc='w', ec='k'))
ax.set_xlim(0, 100)
ax.set_ylim(-2.9, 2.9)
ax.xaxis.set_major_formatter(plt.NullFormatter())
ax.set_ylabel('$h(t)$')
# Bottom: plot the 2D PSD
ax = fig.add_subplot(212)
ax.imshow(wPSD, origin='lower', aspect='auto',
extent=[t[0] + 50, t[-1] + 50, f0[0], f0[-1]],
cmap=plt.cm.binary)
ax.text(0.02, 0.95, ("Wavelet PSD"), color='w',
ha='left', va='top', transform=ax.transAxes)
ax.set_xlim(0, 100)
ax.set_ylim(0.04, 0.6001)
ax.set_xlabel('$t$')
ax.set_ylabel('$f_0$')
plt.show()
for line in trace:
ar = line.split()[0:2]
t.append(float(ar[0]))
speed.append(float(ar[1]))
trace.close()
if (len(t) % 2 != 0):
t = t[1:]
speed = speed[1:]
print ("Starting with %lf, %lf" % (t[0], speed[0]))
print (" ..and going on for %d records" % len(t))
f0 = np.linspace(0.1, 1.0, 100)
wpsd = wavelet_PSD(t, speed, f0, Q=1.0)
out = open("wpsd.txt", "w")
for row in wpsd:
for val in row:
out.write("%lf " % val)
out.write("\n")
out.close()
next_cmd = "gnuplot " + cur_path + "plot-dwt.gnuplot"
print("plotting with command: " + next_cmd)
if (os.system(next_cmd) != 0):
print("Error: can't run command in shell: " + next_cmd)
quit()
p = re.compile(".*\.log$")