Header FstatisticTools.h

Detailed Description

Functions to estimate amplitude parameters and convert between different parametrizations.

Authors

Reinhard Prix

Prototypes
int	XLALEstimatePulsarAmplitudeParams (PulsarCandidate *pulsarParams, const LIGOTimeGPS *FaFb_refTime, const COMPLEX8 Fa, const COMPLEX8 Fb, const AntennaPatternMatrix *Mmunu)
	Estimate the amplitude parameters of a pulsar CW signal, given its phase parameters, constituent parts of the \( \mathcal{F} \) -statistic, and antenna pattern matrix. More...
int	XLALAmplitudeParams2Vect (PulsarAmplitudeVect A_Mu, const PulsarAmplitudeParams Amp)
	Convert amplitude params from 'physical' coordinates \( (h_0, \cos\iota, \psi, \phi_0) \) into 'canonical' coordinates \( A^\mu = (A_1, A_2, A_3, A_4) \) . More...
int	XLALAmplitudeVect2Params (PulsarAmplitudeParams *Amp, const PulsarAmplitudeVect A_Mu)
	Compute amplitude params \( (h_0, \cos\iota, \psi, \phi_0) \) from amplitude-vector \( A^\mu = (A_1, A_2, A_3, A_4) \) . More...
REAL8	XLALComputeOptimalSNR2FromMmunu (const PulsarAmplitudeParams pap, const AntennaPatternMatrix Mmunu)
	Calculates the 'optimal' / perfect-match squared signal-to-noise ratio (SNR^2) for a CW signal for given PulsarAmplitudeParameters 'pap' and Antenna Pattern Matrix 'Mmunu'. More...

Function Documentation

XLALEstimatePulsarAmplitudeParams()

int XLALEstimatePulsarAmplitudeParams	(	PulsarCandidate *	pulsarParams,
		const LIGOTimeGPS *	FaFb_refTime,
		const COMPLEX8	Fa,
		const COMPLEX8	Fb,
		const AntennaPatternMatrix *	Mmunu
	)

Estimate the amplitude parameters of a pulsar CW signal, given its phase parameters, constituent parts of the \( \mathcal{F} \) -statistic, and antenna pattern matrix.

Note

Parameter-estimation based on large parts on Yousuke's notes and implemention (in CFSv1), extended for error-estimation.

Parameters

[in,out]	pulsarParams	Pulsar candidate parameters.
[in]	FaFb_refTime	Reference time of \( F_a \) and \( F_b \) , may differ from pulsar candidate reference time.
[in]	Fa	Complex \( \mathcal{F} \) -statistic amplitude \( F_a \) .
[in]	Fb	Complex \( \mathcal{F} \) -statistic amplitude \( F_b \) .
[in]	Mmunu	Antenna pattern matrix \( M_{\mu\nu} \) .

Definition at line 54 of file FstatisticTools.c.

XLALAmplitudeParams2Vect()

int XLALAmplitudeParams2Vect	(	PulsarAmplitudeVect	A_Mu,
		const PulsarAmplitudeParams	Amp
	)

Convert amplitude params from 'physical' coordinates \( (h_0, \cos\iota, \psi, \phi_0) \) into 'canonical' coordinates \( A^\mu = (A_1, A_2, A_3, A_4) \) .

The equations can be found in [9] or [20] Eq.(2).

Parameters

[out]	A_Mu	Canonical amplitude coordinates \( A^\mu = (A_1, A_2, A_3, A_4) \) .
[in]	Amp	Physical amplitude params \( (h_0, \cos\iota, \psi, \phi_0) \) .

Definition at line 288 of file FstatisticTools.c.

XLALAmplitudeVect2Params()

int XLALAmplitudeVect2Params	(	PulsarAmplitudeParams *	Amp,
		const PulsarAmplitudeVect	A_Mu
	)

Compute amplitude params \( (h_0, \cos\iota, \psi, \phi_0) \) from amplitude-vector \( A^\mu = (A_1, A_2, A_3, A_4) \) .

Adapted from algorithm in XLALEstimatePulsarAmplitudeParams().

Parameters

[out]	Amp	Physical amplitude params \( (h_0, \cos\iota, \psi, \phi_0) \) .
[in]	A_Mu	Canonical amplitude coordinates \( A^\mu = (A_1, A_2, A_3, A_4) \) .

Definition at line 316 of file FstatisticTools.c.

XLALComputeOptimalSNR2FromMmunu()

REAL8 XLALComputeOptimalSNR2FromMmunu	(	const PulsarAmplitudeParams	pap,
		const AntennaPatternMatrix	Mmunu
	)

Calculates the 'optimal' / perfect-match squared signal-to-noise ratio (SNR^2) for a CW signal for given PulsarAmplitudeParameters 'pap' and Antenna Pattern Matrix 'Mmunu'.

The computed 'SNR' is related to the expectation value of the coherent F-statistic 'F' via E[2F] = 4 + SNR^2 for a template perfectly matching the signal, ie SNR^2 = (signal|signal).

Parameters

[in]	pap	PulsarAmplitudeParameter {aPlus, aCross, psi, phi0}
[in]	Mmunu	Antenna-pattern Matrix

Definition at line 398 of file FstatisticTools.c.