# Signal Processing with GW150914¶

Here are some interesting examples of how to process LIGO data using GW150914 as an example.

## Plotting the whitened strain¶

```import matplotlib.pyplot as pp
from pycbc.filter import highpass_fir, lowpass_fir
from pycbc.psd import welch, interpolate
from pycbc.catalog import Merger

for ifo in ['H1', 'L1']:
# Read data and remove low frequency content
h1 = Merger("GW150914").strain(ifo)
h1 = highpass_fir(h1, 15, 8)

# Calculate the noise spectrum
psd = interpolate(welch(h1), 1.0 / h1.duration)

# whiten
white_strain = (h1.to_frequencyseries() / psd ** 0.5).to_timeseries()

# remove some of the high and low
smooth = highpass_fir(white_strain, 35, 8)
smooth = lowpass_fir(smooth, 300, 8)

# time shift and flip L1
if ifo == 'L1':
smooth *= -1
smooth.roll(int(.007 / smooth.delta_t))

pp.plot(smooth.sample_times, smooth, label=ifo)

pp.legend()
pp.xlim(1126259462.21, 1126259462.45)
pp.ylim(-150, 150)
pp.ylabel('Smoothed-Whitened Strain')
pp.grid()
pp.xlabel('GPS Time (s)')
pp.show()
```

## Calculate the signal-to-noise¶

```import matplotlib.pyplot as pp
from urllib.request import urlretrieve
from pycbc.filter import highpass_fir, matched_filter
from pycbc.waveform import get_fd_waveform
from pycbc.psd import welch, interpolate

# Read data and remove low frequency content
fname = 'H-H1_LOSC_4_V2-1126259446-32.gwf'
url = "https://www.gwosc.org/GW150914data/" + fname
urlretrieve(url, filename=fname)
h1 = highpass_fir(h1, 15, 8)

# Calculate the noise spectrum
psd = interpolate(welch(h1), 1.0 / h1.duration)

# Generate a template to filter with
hp, hc = get_fd_waveform(approximant="IMRPhenomD", mass1=40, mass2=32,
f_lower=20, delta_f=1.0/h1.duration)
hp.resize(len(h1) // 2 + 1)

# Calculate the complex (two-phase SNR)
snr = matched_filter(hp, h1, psd=psd, low_frequency_cutoff=20.0)

# Remove regions corrupted by filter wraparound
snr = snr[len(snr) // 4: len(snr) * 3 // 4]

pp.plot(snr.sample_times, abs(snr))
pp.ylabel('signal-to-noise')
pp.xlabel('GPS Time (s)')
pp.show()
```

## Listen to GW150914 in Hanford¶

Here we’ll make a frequency shifted and slowed version of GW150914 as it can be heard in the Hanford data.

```from pycbc.frame import read_frame
from pycbc.filter import highpass_fir, lowpass_fir
from pycbc.psd import welch, interpolate
from pycbc.types import TimeSeries
try:
from urllib.request import urlretrieve
except ImportError:  # python < 3
from urllib import urlretrieve

# Read data and remove low frequency content
fname = 'H-H1_LOSC_4_V2-1126259446-32.gwf'
url = "https://www.gwosc.org/GW150914data/" + fname
urlretrieve(url, filename=fname)
h1 = highpass_fir(read_frame(fname, 'H1:LOSC-STRAIN'), 15.0, 8)

# Calculate the noise spectrum and whiten
psd = interpolate(welch(h1), 1.0 / 32)
white_strain = (h1.to_frequencyseries() / psd ** 0.5 * psd.delta_f).to_timeseries()

# remove some of the high and low frequencies
smooth = highpass_fir(white_strain, 25, 8)
smooth = lowpass_fir(white_strain, 250, 8)

#strech out and shift the frequency upwards to aid human hearing
fdata = smooth.to_frequencyseries()
fdata.roll(int(1200 / fdata.delta_f))
smooth = TimeSeries(fdata.to_timeseries(), delta_t=1.0/1024)

#Take slice around signal
smooth = smooth[len(smooth)//2 - 1500:len(smooth)//2 + 3000]
smooth.save_to_wav('gw150914_h1_chirp.wav')

```

`The audio`