Detailed Description

Functions to calculate the moment of the noise power spectral density.

Author: Brown, D. A., Cokelaer, T. and Sathyaprakash, B. S.

The moments of the noise curve are defined as

\begin{equation} I(q) \equiv S_{h}(f_{0}) \int^{f_{c}/f_{0}}_{f_{s}/f_{0}} \frac{x^{-q}}{S_{h}(x)} \, dx \,. \end{equation}

Because in practice we will always divide one of these moments by another, we do not need to include the \(S_{h}(f_{0})\) term, which always cancels. This function calculates the integral

\begin{equation} I = \int^{f_{c}/f_{0}}_{f_{s}/f_{0}} \frac{x^{-q}}{S_{h}(x)} \, dx \,. \end{equation}

It then divides this quantity by a normalisation constant which has been passed to the function. In the case of calculating the components of the metric for the signal manifold for the purpose of generating a template bank, this constant is given by \(I(7)\), because of the definition of the quantity

\begin{equation} J(q) \equiv \frac{I(q)}{I(7/3)} \,. \end{equation}

Algorithm

Given the exponent pars.ndx and limits of integration pars.xmin and pars.xmax this function returns the moment of the power spectral density specified by the frequency series pars.shf according to

\begin{equation} \mathtt{moment} = \int_{\mathtt{xmin}}^{\mathtt{xmax}} \frac{x^{-\mathtt{ndx}}}{S_h(x)}\, dx \, . \end{equation}

Prototypes
void	LALGetInspiralMoments (LALStatus status, InspiralMomentsEtc moments, REAL8FrequencySeries psd, InspiralTemplate params)

int	XLALGetInspiralMoments (InspiralMomentsEtc moments, REAL8 fLower, REAL8 fCutoff, REAL8FrequencySeries psd)

void	LALGetInspiralMomentsBCV (LALStatus status, InspiralMomentsEtcBCV moments, REAL8FrequencySeries psd, InspiralTemplate params)

void	LALInspiralMoments (LALStatus status, REAL8 moment, InspiralMomentsIn pars)

REAL8	XLALInspiralMoments (REAL8 xmin, REAL8 xmax, REAL8 ndx, REAL8 norm, REAL8FrequencySeries *shf)

Function Documentation

◆ LALGetInspiralMoments()

void LALGetInspiralMoments	(	LALStatus *	status,
		InspiralMomentsEtc *	moments,
		REAL8FrequencySeries *	psd,
		InspiralTemplate *	params
	)

See also: See Module LALInspiralMoments.c for documentation

Definition at line 66 of file LALInspiralMoments.c.

◆ XLALGetInspiralMoments()

int XLALGetInspiralMoments	(	InspiralMomentsEtc *	moments,
		REAL8	fLower,
		REAL8	fCutoff,
		REAL8FrequencySeries *	psd
	)

Definition at line 86 of file LALInspiralMoments.c.

◆ LALGetInspiralMomentsBCV()

void LALGetInspiralMomentsBCV	(	LALStatus *	status,
		InspiralMomentsEtcBCV *	moments,
		REAL8FrequencySeries *	psd,
		InspiralTemplate *	params
	)

See also: See Module LALInspiralMoments.c for documentation

Definition at line 155 of file LALInspiralMoments.c.

◆ LALInspiralMoments()

void LALInspiralMoments	(	LALStatus *	status,
		REAL8 *	moment,
		InspiralMomentsIn	pars
	)

See also: See Module LALInspiralMoments.c for documentation

Parameters

	status	LAL status pointer
[out]	moment	the value of the moment
[in]	pars	input parameters

Definition at line 276 of file LALInspiralMoments.c.

◆ XLALInspiralMoments()

REAL8 XLALInspiralMoments	(	REAL8	xmin,
		REAL8	xmax,
		REAL8	ndx,
		REAL8	norm,
		REAL8FrequencySeries *	shf
	)

Definition at line 294 of file LALInspiralMoments.c.