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LALSimulation 6.2.0.1-5e288d3
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LALSimulation 6.2.0.1-5e288d3
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Miscellaneous routines.
Prototypes | |
| double | XLALMeasureStandardSirenSenseMonitorRange (const REAL8FrequencySeries *psd, double f_min, double f_max) |
| Computes the sense-monitor range for a binary neutron star standard siren signal for a given one-sided detector noise power spectral density. More... | |
| double | XLALMeasureStandardSirenHorizonDistance (const REAL8FrequencySeries *psd, double f_min, double f_max) |
| Computes the horizon distance for a binary neutron star standard siren signal for a given one-sided detector noise power spectral density. More... | |
| double | XLALMeasureStandardSirenSNR (const REAL8FrequencySeries *psd, double f_min, double f_max) |
| Computes the characteristic signal-to-noise for a binary neutron star standard siren signal located at an effective distance of 1 Mpc for a given one-sided detector noise power spectral density. More... | |
| double | XLALMeasureSNRFD (const COMPLEX16FrequencySeries *htilde, const REAL8FrequencySeries *psd, double f_min, double f_max) |
| Measures the characteristic signal-to-noise ratio of a gravitational waveform represented in the frequency domain. More... | |
| double | XLALMeasureSNR (const REAL8TimeSeries *h, const REAL8FrequencySeries *psd, double f_min, double f_max) |
| Measures the characteristic signal-to-noise ratio of a gravitational waveform. More... | |
Macros | |
| #define | LAL_HORIZON_DISTANCE_OVER_SENSEMON_RANGE 2.26478 |
| Ratio of horizon distance to sense-monitor range. More... | |
| double XLALMeasureStandardSirenSenseMonitorRange | ( | const REAL8FrequencySeries * | psd, |
| double | f_min, | ||
| double | f_max | ||
| ) |
Computes the sense-monitor range for a binary neutron star standard siren signal for a given one-sided detector noise power spectral density.
The "Standard Siren" is a restricted (0 pN in amplitude) gravitational waveform produced by a binary neutron star system comprised of two neutron stars, each having a mass of 1.4 Msun. A circular inspiral of point particles is also assumed. The "Sense-Monitor Range" is corresponds to the range measure reported by the LIGO control room monitor SenseMonitor. This range is the radius of a sphere that has contains as many sources as the number that would produce a characteristic signal-to-noise ratio 8 in a detector under the assumption of a homogeneous distribution of sources having random orientations. No cosmological effects are included in this sense-monitor range measure. The sense-monitor range \(\cal R\) is related to the horizon distance \(D_{\rm hor}\) by \(D_{\rm hor} \approx 2.26478\cal R\).
\[ f_{\rm isco} = \frac{c^3}{\pi 6^{3/2} G M} = 1570 {\rm Hz} \]
where \(M=2.8M_\odot\). Iff_max is above this ISCO frequency, or negative, then the ISCO frequency is used; otherwise f_max is used.See XLALMeasureStandardSirenHorizonDistance() for a description of the horizon distance.
See XLALMeasureSNRFD() for further discussion about characteristic signal-to-noise ratios.
| [in] | psd | The one-sided detector strain noise power spectral density. |
| [in] | f_min | The lower bound of the frequency band over which the signal-to-noise ratio will be computed; set to 0 or a negative value for no lower bound. |
| [in] | f_max | The upper bound of the frequency band over which the signal-to-noise ratio will be computed; set to a negative value for no upper bound. |
| LAL_REAL8_FAIL_NAN | Failure. |
Definition at line 179 of file LALSimUtils.c.
| double XLALMeasureStandardSirenHorizonDistance | ( | const REAL8FrequencySeries * | psd, |
| double | f_min, | ||
| double | f_max | ||
| ) |
Computes the horizon distance for a binary neutron star standard siren signal for a given one-sided detector noise power spectral density.
The "Standard Siren" is a restricted (0 pN in amplitude) gravitational waveform produced by a binary neutron star system comprised of two neutron stars, each having a mass of 1.4 Msun. A circular inspiral of point particles is also assumed. The horizon distance is the distance at which such a system that is optimally oriented (face on) and located (at an interferometer's zenith) would induce a characteristic signal-to-noise ratio of 8. No cosmological effects are included in this horizon distance measure.
\[ f_{\rm isco} = \frac{c^3}{\pi 6^{3/2} G M} = 1570 {\rm Hz} \]
where \(M=2.8M_\odot\). Iff_max is above this ISCO frequency, or negative, then the ISCO frequency is used; otherwise f_max is used.See XLALMeasureSNRFD() for further discussion about characteristic signal-to-noise ratios.
| [in] | psd | The one-sided detector strain noise power spectral density. |
| [in] | f_min | The lower bound of the frequency band over which the signal-to-noise ratio will be computed; set to 0 or a negative value for no lower bound. |
| [in] | f_max | The upper bound of the frequency band over which the signal-to-noise ratio will be computed; set to a negative value for no upper bound. |
| LAL_REAL8_FAIL_NAN | Failure. |
Definition at line 236 of file LALSimUtils.c.
| double XLALMeasureStandardSirenSNR | ( | const REAL8FrequencySeries * | psd, |
| double | f_min, | ||
| double | f_max | ||
| ) |
Computes the characteristic signal-to-noise for a binary neutron star standard siren signal located at an effective distance of 1 Mpc for a given one-sided detector noise power spectral density.
The "Standard Siren" is a restricted (0 pN in amplitude) gravitational waveform produced by a binary neutron star system comprised of two neutron stars, each having a mass of 1.4 Msun, that is optimally oriented (face on) and located (at an interferometer's zenith) at a distance of 1 Mpc. A circular inspiral of point particles is also assumed. No cosmological effects are included in this standard siren.
\[ f_{\rm isco} = \frac{c^3}{\pi 6^{3/2} G M} = 1570 {\rm Hz} \]
where \(M=2.8M_\odot\). Iff_max is above this ISCO frequency, or negative, then the ISCO frequency is used; otherwise f_max is used.Implements Eq. (D1) of FINDCHIRP for a 1.4 Msun + 1.4 Msun binary neutron star standard siren at an effective distance 1 Mpc, but with the specified limits on the integral.
| [in] | psd | The one-sided detector strain noise power spectral density. |
| [in] | f_min | The lower bound of the frequency band over which the signal-to-noise ratio will be computed; set to 0 or a negative value for no lower bound. |
| [in] | f_max | The upper bound of the frequency band over which the signal-to-noise ratio will be computed; set to a negative value for the Schwarzschild ISCO upper bound. |
| LAL_REAL8_FAIL_NAN | Failure. |
Definition at line 297 of file LALSimUtils.c.
| double XLALMeasureSNRFD | ( | const COMPLEX16FrequencySeries * | htilde, |
| const REAL8FrequencySeries * | psd, | ||
| double | f_min, | ||
| double | f_max | ||
| ) |
Measures the characteristic signal-to-noise ratio of a gravitational waveform represented in the frequency domain.
This routine measures the characteristic signal-to-noise ratio of a signal htilde for a detector with a given strain noise power spectral density psd. Only frequency components of the signal between f_mim and f_max are included in this measurement. If f_min is zero or negative, no lower bound is imposed. If f_max is negative, no upper bound is imposed.
The term characteristic is used to indicate that this signal-to-noise ratio is the expected value of the signal-to-noise ratio that would be measured for that signal my a perfectly-matched filter in a detector having stationary Gaussian noise with the specified power spectral density. The signal-to-noise ratio actually recorded by a matched filter is a random variable that depends on the particular instance of the noise. Thus the characteristic signal-to-noise ratio returned by this routine is a property of the signal and the statistical properties of the detector noise.
The square of the signal-to-noise ratio is given by
\[ (\mbox{signal-to-noise ratio})^2 = 4 \int_{f_{\rm min}}^{f_{\rm max}} \frac{|\tilde{h}(f)|^2}{S_h(f)}\,df \]
where \(S_h(f)\) is the one-sided detector strain noise power spectral density and \(\tilde{h}(f)\) is the Fourier transform of the signal strain time series \(h(t)\)
\[ \tilde{h}(f) = \int_{-\infty}^\infty h(t) e^{-2\pi ift}\,dt. \]
The one-sided strain noise power spectral density is defined by \(\langle\tilde{n}(f)\tilde{n}^\ast(f')\rangle=\frac{1}{2}S_h(|f|)\delta(f-f')\) where \(\tilde{n}(f)\) is the Fourier transform of the detector noise process \(n(t)\).
The discrete versions of these equations are
\[ (\mbox{signal-to-noise ratio})^2 = 4 \Delta f \sum_{k=k_{\rm min}}^{k_{\rm max}} |\tilde{h}[k]|^2 / S_h[k] \]
where \(\tilde{h}[k]\) for \(0\le k<N\) is the discrete Fourier transform of the discrete time series \(h[j]=h(j\Delta t)\) for \(0\le j<N\):
\[ \tilde{h}[k] = \Delta t \sum_{j=0}^{N-1} h[j] e^{-2\pi ijk/N} \]
(note the factor of \(\Delta t\)). Here \(\Delta t\) is the sampling interval in time, \(\Delta f=1/(N\Delta t)\) is the sampling interval in frequency, and \(N\) is the number of points in the time series. The discrete one-sided detector strain noise power spectral density is \(S_h[k]=2\Delta f\langle|\tilde{n}[k]|^2\rangle\) where \(\tilde{n}[k]\) is the discrete Fourier transform of the detector noise process \(n[j]\).
The limits of the summation are \(k_{\rm min}=f_{\rm min}/\Delta f\) and \(k_{\rm max}=f_{\rm max}/\Delta f\), both rounded to the nearest integer. If \(k_{\rm min}\) is less than 0, it is set to 0. If \(k_{\rm max}\) is negative or greater than \(N/2\) rounded down, it is set to \(N/2\) rounded down. This ends up double-counting the DC and a possible Nyquist component, but it is assumed these terms have negligible contribution to the sum and there is no special case to handle them separately (most likely, the detector will have no sensitivity to those components anyway).
This routine will accept frequency series \(\tilde{h}\) and \(S_h\) that have different frequency resolutions (i.e., different \(\Delta f\)). In this case, a new frequency series \(S_h\) is computed with the same resolution as \(\tilde{h}\) by interpolation. A simple linear interpolation in the logarithm of the power spectral density is used. Any points where the power spectral density is zero are considered to be invalid and are omitted from the sum.
| [in] | htilde | The Fourier transform of the signal strain. |
| [in] | psd | The one-sided detector strain noise power spectral density. |
| [in] | f_min | The lower bound of the frequency band over which the signal-to-noise ratio will be computed; set to 0 or a negative value for no lower bound. |
| [in] | f_max | The upper bound of the frequency band over which the signal-to-noise ratio will be computed; set to a negative value for no upper bound. |
| LAL_REAL8_FAIL_NAN | Failure. |
Definition at line 473 of file LALSimUtils.c.
| double XLALMeasureSNR | ( | const REAL8TimeSeries * | h, |
| const REAL8FrequencySeries * | psd, | ||
| double | f_min, | ||
| double | f_max | ||
| ) |
Measures the characteristic signal-to-noise ratio of a gravitational waveform.
This routine measures the characteristic signal-to-noise ratio of a signal h for a detector with a given strain noise power spectral density psd. Only frequency components of the signal between f_mim and f_max are included in this measurement. If f_min is zero or negative, no lower bound is imposed. If f_max is negative, no upper bound is imposed.
A copy of the strain time series h is zero padded up to the next power of two in length and then Fourier transformed; the routine XLALMeasureSNRFD() is then used to compute the characteristic signal-to-noise ratio. See XLALMeasureSNRFD() for further details.
| [in] | h | The strain time series of the signal. |
| [in] | psd | The one-sided detector strain noise power spectral density. |
| [in] | f_min | The lower bound of the frequency band over which the signal-to-noise ratio will be computed; set to 0 or a negative value for no lower bound. |
| [in] | f_max | The upper bound of the frequency band over which the signal-to-noise ratio will be computed; set to a negative value for no upper bound. |
| LAL_REAL8_FAIL_NAN | Failure. |
Definition at line 587 of file LALSimUtils.c.
| #define LAL_HORIZON_DISTANCE_OVER_SENSEMON_RANGE 2.26478 |
Ratio of horizon distance to sense-monitor range.
This factor is used in XLALMeasureStandardSirenSenseMonitorRange().
sensemon_range = horizon_dist / LAL_HORIZON_DISTANCE_OVER_SENSEMON_RANGE
The factor can be computed using Monte Carlo methods; its value has been found to be 2.264778 +- 0.000002. This constant keeps it to only 5 decimal places however.
Definition at line 56 of file LALSimUtils.h.
1.9.4