<p>A new analysis of gravitational wave (and other data) from GW170817 on 2017-Aug-17 has been published, strongly suggesting that the merger of two neutron stars resulted in a large, rapidly rotating neutron star, rather than a black hole. From the abstract of the recent <em>open access Letter in MNRAS</em> <a href="https://academic.oup.com/mnrasl/article/482/1/L46/5090425" rel="nofollow noreferrer">Observational evidence for extended emission to GW170817</a>:</p>
<blockquote>
<p>[...]Here, we report on a possible detection of extended emission (EE) in gravitational radiation during GRB170817A: a descending chirp with characteristic time-scale τs = 3.01 ± 0.2 s in a (H1,L1)-spectrogram up to 700 Hz with Gaussian equivalent level of confidence greater than 3.3σ based on causality alone following edge detection applied to (H1,L1)-spectrograms merged by frequency coincidences. Additional confidence derives from the strength of this EE. The observed frequencies below 1 kHz indicate a hypermassive magnetar rather than a black hole, spinning down by magnetic winds and interactions with dynamical mass ejecta.</p>
</blockquote>
<p>Maurice H P M van Putten and Massimo Della Valle,
Monthly Notices of the Royal Astronomical Society: Letters, Volume 482, Issue 1, 1 January 2019, Pages L46–L49, <a href="https://doi.org/10.1093/mnrasl/sly166" rel="nofollow noreferrer">https://doi.org/10.1093/mnrasl/sly166</a></p>
<p>Discussion in paper points to <a href="https://academic.oup.com/mnrasl/article/482/1/L46/5090425#supplementary-data" rel="nofollow noreferrer">supplementary data</a> and in the introduction to that document, it says:</p>
<blockquote>
<p>For GW170817A/GRB170817A, we perform a model-independent deep search for broadband extended gravitational-wave emission in 2048 s (LIGO 2017) of data at 4096 Hz according to Fig. A1 comprising</p>
<ul>
<li>Pre-processing: cleaning and glitch removal (Abbott et al. 2017a) followed by whitening of H1, L1 and V1 data;</li>
<li><strong>Singe detector spectrograms by GPU-accelerated butterfly filtering of H1, L1 and V1 by matched filtering over a dense bank of time-symmetric chirp-like templates</strong> (van Putten et al. 2014; van Putten 2017);</li>
<li>Merging spectrograms by coincidences in frequency or amplitude, producing merged spectrograms as input to image analysis (van Putten 2018).</li>
</ul>
</blockquote>
<p>I am having trouble understanding what <em>GPU-accelerated butterfly filtering of H1, L1 and V1 by matched filtering over a dense bank of time-symmetric chirp-like templates</em> means. <code>van Putten et al. 2014</code> in the supplementary data document refers to both <a href="http://iopscience.iop.org/article/10.1088/0004-637X/786/2/146" rel="nofollow noreferrer">BROADBAND TURBULENT SPECTRA IN GAMMA-RAY BURST LIGHT CURVES</a> and to <a href="http://iopscience.iop.org/article/10.3847/0004-637X/819/2/169" rel="nofollow noreferrer"></a> as well. These appear to be thorough explanations, but pretty in-depth.</p>
<p><strong>Question:</strong> Is it possible to explain the basics of what &quot;GPU-accelerated butterfly filtering of H1, L1 and V1 by matched filtering over a dense bank of time-symmetric chirp-like templates&quot; means? A dense bank of chirp-like templates sounds like it could be analogous to a wavelet-type analysis, but with basis waveforms tailored to this specific problem.</p>
<p>First image is a cropped and annotated version of the second which ia from <a href="https://academic.oup.com/mnrasl/article/482/1/L46/5090425" rel="nofollow noreferrer">here</a>.</p>
<p><a href="https://i.sstatic.net/JF6wh.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/JF6wh.png" alt="enter image description here" /></a></p>
<p><a href="https://i.sstatic.net/TKBhp.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/TKBhp.png" alt="enter image description here" /></a></p>
<blockquote>
<p>Figure2. Ascending–descending chirp in the (H1,L1)-spectrogram produced by the double neutron star merger GW170817 concurrent with GRB170817A (Goldstein et al. 2017) past coalescence (tc = 1842.43 s). Minor accompanying features around 100 Hz ( 1840-1852 s) are conceivably due to dynamical mass ejecta. Colour coding (blue-to-yellow) is proportional to amplitude defined by butterfly output ρ of time-symmetric chirp-like template correlations to data.</p>
</blockquote>

CC BY-SA 4.0
2018-11-16T13:48:50.897Z
GPU-accelerated butterfly filtering is a computer-program filtering algorithm, to filter only signals out of the data.

time-symmetric chirp-like templates are templates of signals of various types (both GW and non GW).

The detection algorithm of the GW is that, the system has a library (i.e., a dense bank) of various known types of signals, and how they would look like. From that, once you have data you can compute detection probability like false-alarm one.
Kornpob Bhirombhakdi
CC BY-SA 4.0
2018-11-16T15:03:11.457Z
@KornpobBhirombhakdi thanks! That's an excellent functional summary and I appreciate it. I am hoping that when an answer is posted, it will explain a bit more of the mathematical aspects. For example, I certainly understand that "chirp-like templates are templates of signals of various types" but that's a bit circular. I'm also comfortable with using a library search (rather than an optimization using a basis set) and so that is very helpful. I wonder what one template might "look like". Would it be simply a 1 millisecond long strain waveform?
uhoh
CC BY-SA 4.0
2018-12-05T08:41:01.590Z
@KornpobBhirombhakdi if you know of (or can find) a reference that describes how the library is built, that might help towards finding an answer. I can read it and then post an answer myself if nobody else is interested. Thanks!
uhoh
CC BY-SA 4.0
2018-12-05T16:25:31.223Z
have you checked this paper, Abbott B. P. et al., 2017a, Phys. Rev. Lett., 119, 161101? In section 2. Data, there are references about the data processing. And, section 3 desbribes stuff leading to the false alarm rate at the end.
Kornpob Bhirombhakdi
CC BY-SA 4.0
2018-12-05T16:53:54.000Z
@KornpobBhirombhakdi I did talk about the results of Abbot 2017 [here](https://astronomy.stackexchange.com/a/20694/7982) but I will go back now and have a look in section 2 (and 3) and references therein, thank you!
uhoh
<observational-astronomy><gravitational-waves><neutron-star>
What does "GPU-accelerated butterfly matched filtering over dense bank of time-symmetric chirp-like templates" mean? (GW170817)
uhoh
# What does "GPU-accelerated butterfly matched filtering over dense bank of time-symmetric chirp-like templates" mean? (GW170817)

(Asked by: username_0 on 2018-11-16)

A new analysis of gravitational wave (and other data) from GW170817 on 2017-Aug-17 has been published, strongly suggesting that the merger of two neutron stars resulted in a large, rapidly rotating neutron star, rather than a black hole. From the abstract of the recent *open access Letter in MNRAS* [Observational evidence for extended emission to GW170817](https://academic.oup.com/mnrasl/article/482/1/L46/5090425):

> [...]Here, we report on a possible detection of extended emission (EE) in gravitational radiation during GRB170817A: a descending chirp with characteristic time-scale τs = 3.01 ± 0.2 s in a (H1,L1)-spectrogram up to 700 Hz with Gaussian equivalent level of confidence greater than 3.3σ based on causality alone following edge detection applied to (H1,L1)-spectrograms merged by frequency coincidences. Additional confidence derives from the strength of this EE. The observed frequencies below 1 kHz indicate a hypermassive magnetar rather than a black hole, spinning down by magnetic winds and interactions with dynamical mass ejecta.

Maurice H P M van Putten and Massimo Della Valle,
Monthly Notices of the Royal Astronomical Society: Letters, Volume 482, Issue 1, 1 January 2019, Pages L46–L49, <https://doi.org/10.1093/mnrasl/sly166>

Discussion in paper points to [supplementary data](https://academic.oup.com/mnrasl/article/482/1/L46/5090425#supplementary-data) and in the introduction to that document, it says:

> For GW170817A/GRB170817A, we perform a model-independent deep search for broadband extended gravitational-wave emission in 2048 s (LIGO 2017) of data at 4096 Hz according to Fig. A1 comprising
>
> * Pre-processing: cleaning and glitch removal (Abbott et al. 2017a) followed by whitening of H1, L1 and V1 data;
> * **Singe detector spectrograms by GPU-accelerated butterfly filtering of H1, L1 and V1 by matched filtering over a dense bank of time-symmetric chirp-like templates** (van Putten et al. 2014; van Putten 2017);
> * Merging spectrograms by coincidences in frequency or amplitude, producing merged spectrograms as input to image analysis (van Putten 2018).

I am having trouble understanding what *GPU-accelerated butterfly filtering of H1, L1 and V1 by matched filtering over a dense bank of time-symmetric chirp-like templates* means. `van Putten et al. 2014` in the supplementary data document refers to both [BROADBAND TURBULENT SPECTRA IN GAMMA-RAY BURST LIGHT CURVES](http://iopscience.iop.org/article/10.1088/0004-637X/786/2/146) and to  as well. These appear to be thorough explanations, but pretty in-depth.

**Question:** Is it possible to explain the basics of what "GPU-accelerated butterfly filtering of H1, L1 and V1 by matched filtering over a dense bank of time-symmetric chirp-like templates" means? A dense bank of chirp-like templates sounds like it could be analogous to a wavelet-type analysis, but with basis waveforms tailored to this specific problem.

First image is a cropped and annotated version of the second which ia from [here](https://academic.oup.com/mnrasl/article/482/1/L46/5090425).

[![enter image description here](https://i.sstatic.net/JF6wh.png)](https://i.sstatic.net/JF6wh.png)

[![enter image description here](https://i.sstatic.net/TKBhp.png)](https://i.sstatic.net/TKBhp.png)

> Figure2. Ascending–descending chirp in the (H1,L1)-spectrogram produced by the double neutron star merger GW170817 concurrent with GRB170817A (Goldstein et al. 2017) past coalescence (tc = 1842.43 s). Minor accompanying features around 100 Hz ( 1840-1852 s) are conceivably due to dynamical mass ejecta. Colour coding (blue-to-yellow) is proportional to amplitude defined by butterfly output ρ of time-symmetric chirp-like template correlations to data.

**Tags:** observational-astronomy, gravitational-waves, neutron-star

> **Comments:**
> **username_1**: GPU-accelerated butterfly filtering is a computer-program filtering algorithm, to filter only signals out of the data.  time-symmetric chirp-like templates are templates of signals of various types (both GW and non GW).  The detection algorithm of the GW is that, the system has a library (i.e., a dense bank) of various known types of signals, and how they would look like. From that, once you have data you can compute detection probability like false-alarm one.  
> **username_0**: @KornpobBhirombhakdi thanks! That's an excellent functional summary and I appreciate it. I am hoping that when an answer is posted, it will explain a bit more of the mathematical aspects. For example, I certainly understand that "chirp-like templates are templates of signals of various types" but that's a bit circular. I'm also comfortable with using a library search (rather than an optimization using a basis set) and so that is very helpful. I wonder what one template might "look like". Would it be simply a 1 millisecond long strain waveform?  
> **username_0**: @KornpobBhirombhakdi if you know of (or can find) a reference that describes how the library is built, that might help towards finding an answer. I can read it and then post an answer myself if nobody else is interested. Thanks!  
> **username_1**: have you checked this paper, Abbott B. P. et al., 2017a, Phys. Rev. Lett., 119, 161101? In section 2. Data, there are references about the data processing. And, section 3 desbribes stuff leading to the false alarm rate at the end.  
> **username_0**: @KornpobBhirombhakdi I did talk about the results of Abbot 2017 [here](https://astronomy.stackexchange.com/a/20694/7982) but I will go back now and have a look in section 2 (and 3) and references therein, thank you!  

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## 0 answers

