# Dynamical Power Spectra (on fake data)¶

[1]:

%matplotlib inline

[2]:

# import some modules
import numpy as np
import matplotlib.pyplot as plt
import stingray

[3]:

# choose style of plots, seaborn-talk produce nice big figures
plt.style.use('seaborn-talk')


## Generate a fake lightcurve¶

[4]:

# Array of timestamps, 10000 bins from 1s to 100s
times = np.linspace(1,100,10000)

# base component of the lightcurve, poisson-like
# the averaged count-rate is 100 counts/bin
noise = np.random.poisson(100,10000)

# time evolution of the frequency of our fake periodic signal
# the frequency changes with a sinusoidal shape around the value 24Hz
freq = 25 + 1.2*np.sin(2*np.pi*times/130)

# Our fake periodic variability with drifting frequency
# the amplitude of this variability is 10% of the base flux
var = 10*np.sin(2*np.pi*freq*times)

# The signal of our lightcurve is equal the base flux plus the variable flux
signal = noise+var

[5]:

# Create the lightcurve object
lc = stingray.Lightcurve(times, signal)


### Visualizing the lightcurve¶

[6]:

lc.plot(labels=['Time (s)', 'Counts / bin'])
plt.title('Lightcurve')

[6]:

<matplotlib.text.Text at 0x7fabaa006630>


### Zomming in..¶

[7]:

lc.plot(labels=['Time (s)', 'Counts / bin'], axis=[20,23,50,160])
plt.title('Zoomed in Lightcurve')

[7]:

<matplotlib.text.Text at 0x7faba9f36e48>


# A power spectrum of this lightcurve..¶

[8]:

ps = stingray.AveragedPowerspectrum(lc, segment_size=3, norm='leahy')

[9]:

plt.plot(ps.freq, ps.power, label='segment size = {}s \n number of segments = {}'.format(3, int(lc.tseg/3)))
plt.title('Averaged Powerspectrum')
plt.xlabel('Frequency (Hz)')
plt.ylabel('Power')
plt.legend()

[9]:

<matplotlib.legend.Legend at 0x7faba9e66d30>


# Let’s look at the Dynamic Powerspectrum..¶

[10]:

dps = stingray.DynamicalPowerspectrum(lc, segment_size=3)

[11]:

extent = min(dps.time), max(dps.time), min(dps.freq), max(dps.freq)
plt.imshow(dps.dyn_ps, aspect="auto", origin="lower", vmax=0.001,
interpolation="none", extent=extent)
plt.title('Dynamic Powerspecttrum')
plt.xlabel('Time (s)')
plt.ylabel('Frequency (Hz)')
plt.colorbar(label='Power')

[11]:

<matplotlib.colorbar.Colorbar at 0x7faba9e3b5c0>


## It is actually only one feature drifiting along time¶

# Rebinning in Frequency

[12]:

print("The current frequency resolution is {}".format(dps.df))

The current frequency resolution is 0.33443708609271494


Let’s rebin to a frequency resolution of 1 Hz and using the average of the power

[13]:

dps.rebin_frequency(df_new=1.0, method="average")

[14]:

print("The new frequency resolution is {}".format(dps.df))

The new frequency resolution is 1.0


Let’s see how the Dynamical Powerspectrum looks now

[15]:

extent = min(dps.time), max(dps.time), min(dps.freq), max(dps.freq)
plt.imshow(dps.dyn_ps, origin="lower", aspect="auto",
interpolation="none", extent=extent)
plt.colorbar()
plt.ylim(15, 30)

[15]:

(15, 30)


# Rebin time¶

Let’s rebin our matrix in the time axis

[16]:

print("The current time resolution is {}".format(dps.dt))

The current time resolution is 3.0


Let’s rebin to a time resolution of 4 s

[17]:

dps.rebin_time(dt_new=4.0, method="average")

[18]:

print("The new time resolution is {}".format(dps.dt))

The new time resolution is 4.0

[19]:

extent = min(dps.time), max(dps.time), min(dps.freq), max(dps.freq)
plt.imshow(dps.dyn_ps, origin="lower", aspect="auto",
interpolation="none", extent=extent)
plt.colorbar()
plt.ylim(15,30)

[19]:

(15, 30)


## Let’s trace that drifiting feature.¶

[20]:

# By looking into the maximum power of each segment
max_pos = dps.trace_maximum()

[21]:

plt.plot(dps.time, dps.freq[max_pos], color='red', alpha=1)
plt.xlabel('Time (s)')
plt.ylabel('Frequency (Hz)')
plt.title('Detected frequency drift')

[21]:

<matplotlib.text.Text at 0x7faba9bb6a90>


# Overlaying this traced function with the Dynamical Powerspectrum¶

[22]:

extent = min(dps.time), max(dps.time), min(dps.freq), max(dps.freq)
plt.imshow(dps.dyn_ps, aspect="auto", origin="lower", vmax=0.001,
interpolation="none", extent=extent, alpha=0.6)
plt.plot(dps.time, dps.freq[max_pos], color='C3', lw=5, alpha=1, label='drifiting function')

plt.ylim(15,30) # zoom-in around 24 hertz

plt.title('Overlay of Drifting fuction and Dynamic Powerspecttrum')
plt.xlabel('Time (s)')
plt.ylabel('Frequency (Hz)')
plt.colorbar(label='Power')
plt.legend()

[22]:

<matplotlib.legend.Legend at 0x7faba9b51358>