Find an Inspiral: Bandpass filter
This tutorial assumes that you have already
read in the data and template from the
Find an Inspiral
Plot an ASD for the data and the template
Can you see the signal in the data? Probably not. The signal
amplitude is much smaller than the
noise amplitude. However, it is possible to recover this
signal because it has more power than the noise at some frequencies.
To see which frequencies, try to plot an ASD of the template and the noise.
You can assume the signal is only in the first 12 seconds of data,
so you can use the last 4 seconds to make an ASD of just noise.
The noise is simulated, colored Gaussian noise, high pass filtered
with a 20 Hz cut-off. The tapering in the template effectively acts
as a high-pass filter above 50 Hz. Between 50 and 200 Hz, the
ASD of the template can be seen to fall with an f^(-7/6) power law, which
is characteristic of inspirals. The "ringdown" can be seen as a small
bump around 210 Hz.
You can see an example of how to plot an ASD in the
Plot Gallery. If you really get
stuck, you can also peak at the
whole script described in this tutorial.
Once you plot your ASD, look to see which frequencies the
template has the most power relative to the noise.
You should see this is true for a range of frequencies near 100 Hz.
See the ASD
Apply a bandpass filter
We bandpass from 80 to 250 Hz, since we are looking for a
signal in that frequency band and the detector noise is pretty
This will keep power in this frequency range,
but suppress power
away from this frequency. You can construct a
butterworth bandpass filter like this:
See the filtered data
(B,A) = sig.butter(4, [80/(fs/2.0), 250/(fs/2.0)], btype='pass')
data_pass = sig.lfilter(B, A, data)
The passband for the filter is between 80 Hz and 250 Hz. Notice
that the passband has to be input as a fraction of the Nyquist
frequency. Try plotting
data_pass, which is the
data after applying the band-pass filter. Do you see any evidence
for the signal now? The peak occurs
at the time when the signal is loudest, near the end of the template.
also download the entire script
described in this tutorial.