This module computes the usual stationary phase approximation to the Fourier transform of a chirp waveform given by Eq. \eqref{eq_InspiralFourierPhase_f2}. More...

Prototypes
static REAL8	XLALInspiralTaylorF2Phasing0PN (REAL8 v, expnCoeffs *ak)

static REAL8	XLALInspiralTaylorF2Phasing2PN (REAL8 v, expnCoeffs *ak)

static REAL8	XLALInspiralTaylorF2Phasing3PN (REAL8 v, expnCoeffs *ak)

static REAL8	XLALInspiralTaylorF2Phasing4PN (REAL8 v, expnCoeffs *ak)

static REAL8	XLALInspiralTaylorF2Phasing5PN (REAL8 v, expnCoeffs *ak)

static REAL8	XLALInspiralTaylorF2Phasing6PN (REAL8 v, expnCoeffs *ak)

static REAL8	XLALInspiralTaylorF2Phasing7PN (REAL8 v, expnCoeffs *ak)

int	XLALInspiralStationaryPhaseApprox2 (REAL4Vector signalvec, InspiralTemplate params)

Detailed Description

This module computes the usual stationary phase approximation to the Fourier transform of a chirp waveform given by Eq. \eqref{eq_InspiralFourierPhase_f2}.

Author: B.S. Sathyaprakash

Prototypes

XLALInspiralStationaryPhaseApprox2()

signalvec: Output containing the inspiral waveform.
params: Input containing binary chirp parameters.

Description

Computes the Fourier transform of the chirp signal in the stationary phase approximation and returns the real and imaginary parts of the Fourier domain signal in the convention of fftw. For a signal vector of length n=signalvec->length (n even):

signalvec->data[0] is the real 0th frequency component of the Fourier transform.
signalvec->data[n/2] is the real Nyquist frequency component of the Fourier transform.
signalvec->data[k] and signalvec->data[n-k], for k=1,..., n/2-1, are the real and imaginary parts of the Fourier transform at a frequency \(k\Delta f=k/T,\) \(T\) being the duration of the signal and \(\Delta f=1/T\) is the frequency resolution.

Algorithm

The standard SPA is given by Eq. \eqref{eq_InspiralFourierPhase_f2}. We define a variable function pointer LALInspiralTaylorF2Phasing and point it to one of the static functions defined within this function that explicitly calculates the Fourier phase at the PN order chosen by the user. The reference points are chosen so that on inverse Fourier transforming the time-domain waveform will

be padded with zeroes in the first params->nStartPad bins,
begin with a phase shift of params->nStartPhase radians,
have an amplitude of \(n v^2.\)

Uses

XLALInspiralSetup()
XLALInspiralChooseModel()
XLALInspiralTaylorF2Phasing[0234567]PN()

Notes

If it is required to compare the output of this module with a time domain signal one should use an inverse Fourier transform routine that packs data in the same way as fftw. Moreover, one should divide the resulting inverse Fourier transform by a factor \(n/2\) to be consistent with the amplitude used in time-domain signal models.

Definition in file LALInspiralStationaryPhaseApprox2.c.

Go to the source code of this file.

Function Documentation

◆ XLALInspiralTaylorF2Phasing0PN()

static REAL8 XLALInspiralTaylorF2Phasing0PN	(	REAL8	v,
		expnCoeffs *	ak
	)

static

Definition at line 223 of file LALInspiralStationaryPhaseApprox2.c.

◆ XLALInspiralTaylorF2Phasing2PN()

static REAL8 XLALInspiralTaylorF2Phasing2PN	(	REAL8	v,
		expnCoeffs *	ak
	)

static

Definition at line 229 of file LALInspiralStationaryPhaseApprox2.c.

◆ XLALInspiralTaylorF2Phasing3PN()

static REAL8 XLALInspiralTaylorF2Phasing3PN	(	REAL8	v,
		expnCoeffs *	ak
	)

static

Definition at line 237 of file LALInspiralStationaryPhaseApprox2.c.

◆ XLALInspiralTaylorF2Phasing4PN()

static REAL8 XLALInspiralTaylorF2Phasing4PN	(	REAL8	v,
		expnCoeffs *	ak
	)

static

Definition at line 245 of file LALInspiralStationaryPhaseApprox2.c.

◆ XLALInspiralTaylorF2Phasing5PN()

static REAL8 XLALInspiralTaylorF2Phasing5PN	(	REAL8	v,
		expnCoeffs *	ak
	)

static

Definition at line 253 of file LALInspiralStationaryPhaseApprox2.c.

◆ XLALInspiralTaylorF2Phasing6PN()

static REAL8 XLALInspiralTaylorF2Phasing6PN	(	REAL8	v,
		expnCoeffs *	ak
	)

static

Definition at line 263 of file LALInspiralStationaryPhaseApprox2.c.

◆ XLALInspiralTaylorF2Phasing7PN()

static REAL8 XLALInspiralTaylorF2Phasing7PN	(	REAL8	v,
		expnCoeffs *	ak
	)

static

Definition at line 277 of file LALInspiralStationaryPhaseApprox2.c.

◆ XLALInspiralStationaryPhaseApprox2()

int XLALInspiralStationaryPhaseApprox2	(	REAL4Vector *	signalvec,
		InspiralTemplate *	params
	)

Definition at line 100 of file LALInspiralStationaryPhaseApprox2.c.