# Improving the efficiency of the detection of gravitational wave signals from inspiraling compact binaries: Chebyshev interpolation

## Abstract

Inspiraling compact-object binary systems are promising gravitational wave sources for ground and space-based detectors. The time-dependent signature of these sources is a well-characterized function of a relatively small number of parameters; thus, the favored analysis technique makes use of matched filtering and maximum likelihood methods. As the parameters that characterize the source model vary, so do the templates against which the detector data are compared in the matched filter. For small variations in the parameters, the filter responses are closely correlated. Current analysis methodology samples a bank of filters whose parameter values are chosen so that the correlation between successive samples from successive filters in the bank is 97%. Correspondingly, the additional information available with each successive template evaluation is, in a real sense, only 3% of that already provided by the nearby templates. The reason for such a dense coverage of parameter space is to minimize the chance that a real signal, near the detection threshold, will be missed by the parameter space sampling. Here we investigate the use of Chebyshev interpolation for reducing the number of templates that must be evaluated to obtain the same analysis sensitivity. Additionally, rather than focus on the 'loss' of signal-to-noise associated withmore »

- Authors:

- Inter-University Centre for Astronomy and Astrophysics, Ganeshkhind, Pune-411 007 (India)
- (United States)

- Publication Date:

- OSTI Identifier:
- 20711515

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.72.102001; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; BINARY STARS; BLACK HOLES; COMPARATIVE EVALUATIONS; CORRELATIONS; DETECTION; EFFICIENCY; GRAVITATIONAL WAVE DETECTORS; GRAVITATIONAL WAVES; INTERPOLATION; MAXIMUM-LIKELIHOOD FIT; NEUTRON STARS; POLYNOMIALS; PROBABILITY; SAMPLING; SENSITIVITY; SIGNAL-TO-NOISE RATIO; SIGNALS; SPACE; TIME DEPENDENCE; VARIATIONS

### Citation Formats

```
Mitra, S., Dhurandhar, S.V., Finn, L.S., and Center for Gravitational Wave Physics, Pennsylvania State University, University Park, Pennsylvania 16802.
```*Improving the efficiency of the detection of gravitational wave signals from inspiraling compact binaries: Chebyshev interpolation*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevD.72.102001.

```
Mitra, S., Dhurandhar, S.V., Finn, L.S., & Center for Gravitational Wave Physics, Pennsylvania State University, University Park, Pennsylvania 16802.
```*Improving the efficiency of the detection of gravitational wave signals from inspiraling compact binaries: Chebyshev interpolation*. United States. doi:10.1103/PhysRevD.72.102001.

```
Mitra, S., Dhurandhar, S.V., Finn, L.S., and Center for Gravitational Wave Physics, Pennsylvania State University, University Park, Pennsylvania 16802. Tue .
"Improving the efficiency of the detection of gravitational wave signals from inspiraling compact binaries: Chebyshev interpolation". United States.
doi:10.1103/PhysRevD.72.102001.
```

```
@article{osti_20711515,
```

title = {Improving the efficiency of the detection of gravitational wave signals from inspiraling compact binaries: Chebyshev interpolation},

author = {Mitra, S. and Dhurandhar, S.V. and Finn, L.S. and Center for Gravitational Wave Physics, Pennsylvania State University, University Park, Pennsylvania 16802},

abstractNote = {Inspiraling compact-object binary systems are promising gravitational wave sources for ground and space-based detectors. The time-dependent signature of these sources is a well-characterized function of a relatively small number of parameters; thus, the favored analysis technique makes use of matched filtering and maximum likelihood methods. As the parameters that characterize the source model vary, so do the templates against which the detector data are compared in the matched filter. For small variations in the parameters, the filter responses are closely correlated. Current analysis methodology samples a bank of filters whose parameter values are chosen so that the correlation between successive samples from successive filters in the bank is 97%. Correspondingly, the additional information available with each successive template evaluation is, in a real sense, only 3% of that already provided by the nearby templates. The reason for such a dense coverage of parameter space is to minimize the chance that a real signal, near the detection threshold, will be missed by the parameter space sampling. Here we investigate the use of Chebyshev interpolation for reducing the number of templates that must be evaluated to obtain the same analysis sensitivity. Additionally, rather than focus on the 'loss' of signal-to-noise associated with the finite number of filters in the template bank, we evaluate the receiver operating characteristic (ROC) as a measure of the effectiveness of an analysis technique. The ROC relates the false alarm probability to the false dismissal probability of an analysis, which are the quantities that bear most directly on the effectiveness of an analysis scheme. As a demonstration, we compare the present 'dense sampling' analysis methodology with the 'interpolation' methodology using Chebyshev polynomials, restricted to one dimension of the multidimensional analysis problem by plotting the ROC curves. We find that the interpolated search can be arranged to have the same false alarm and false dismissal probabilities as the dense sampling strategy using 25% fewer templates. Generalized to the two-dimensional space used in the computationally limited current analyses, this suggests a factor of 2 increase in computational efficiency; generalized to the full seven-dimensional parameter space that characterizes the signal associated with an eccentric binary system of spinning neutron stars or black holes, it suggests an order of magnitude increase in computational efficiency. Since the computational cost of the analysis is driven almost exclusively by the matched filter evaluations, a reduction in the number of template evaluations translates directly into an increase in computational efficiency; additionally, since the computational cost of the analysis is large, the increased efficiency translates also into an increase in the size of the parameter space that can be analyzed and, thus, the science that can be accomplished with the data.},

doi = {10.1103/PhysRevD.72.102001},

journal = {Physical Review. D, Particles Fields},

number = 10,

volume = 72,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}