Header NormalizeSFTRngMed.h

Detailed Description

Header file for SFT normalization routines.

Normalizes SFTs based on their noise floor calculated using the running median.

Author

Krishnan, B.

Date

History: Moved from Hough code 31/7/05

Author

Badri Krishnan and Alicia Sintes

History: Created by B. Krishnan Aug, 2004 Taken from SFTbin.c and PeakSelect.c from Hough code

Description

This module contains functions for normalizing SFTs. Currently two normalizations are supported. Given SFT data \( \tilde{x}_k \) where \( k \) labels a frequency bin, the normalized SFT is either \( \tilde{x}_k/\sqrt{ < |\tilde{x}_k|^2 >} \) or \( \sqrt{2N} \tilde{x}_k/\sqrt{ < |\tilde{x}_k|^2 >} \) , where \( N \) is the number of frequency bins in the SFT. The first normalization ensures that the SFT power follows an exponential distribution with unit mean (if the SFT data is distributed normally), while the second normalization is appropriate in the time domain. In either case, the mean of \( |\tilde{x}_k|^2 \) is estimated using the median, suitably normalized assuming that the power is distributed is exponentially.

Uses

XLALSFTtoPeriodogram ()
XLALPeriodoToRngmed ()
XLALNormalizeSFT ()
XLALNormalizeSFTVect ()
XLALNormalizeMultiSFTVect ()

The function XLALNormalizeSFTVect() takes as input a vector of SFTs and normalizes them. This function calls the functions XLALNormalizeSFT() which normalizes a single SFT, XLALSFTtoPeriodogram() which calculates the \( |\tilde{x}|^2 \) and XLALPeriodoToRngmed () which applies the running median algorithm to find a vector of medians. The function XLALNormalizeMultiSFTVect() normalizes a multi-IFO collection of SFT vectors and also returns a collection of power-estimates for these vectors using the Running median method.

Prototypes
int	XLALSFTtoRngmed (REAL8FrequencySeries *rngmed, const SFTtype *sft, UINT4 blockSize)
	Calculates a smoothed (running-median) periodogram for the given SFT. More...
int	XLALSFTtoPeriodogram (REAL8FrequencySeries *periodo, const COMPLEX8FrequencySeries *SFT)
	Calculate the "periodogram" of an SFT, ie the modulus-squares of the SFT-data. More...
int	XLALPeriodoToRngmed (REAL8FrequencySeries *rngmed, const REAL8FrequencySeries *periodo, UINT4 blockSize)
	Calculates running median over a single periodogram. More...
int	XLALNormalizeSFT (REAL8FrequencySeries *rngmed, SFTtype *sft, UINT4 blockSize, const REAL8 assumeSqrtS)
	Normalize an sft based on RngMed estimated PSD, and returns running-median. More...
int	XLALNormalizeSFTVect (SFTVector *sftVect, UINT4 blockSize, const REAL8 assumeSqrtS)
	Function for normalizing a vector of SFTs. More...
MultiPSDVector *	XLALNormalizeMultiSFTVect (MultiSFTVector *multsft, UINT4 blockSize, const MultiNoiseFloor *assumeSqrtSX)
	Function for normalizing a multi vector of SFTs in a multi IFO search and returns the running-median estimates of the power. More...
int	XLALSFTstoCrossPeriodogram (REAL8FrequencySeries *periodo, const COMPLEX8FrequencySeries *sft1, const COMPLEX8FrequencySeries *sft2)
	Calculate the cross-correlation periodogram from 2 SFTs. More...

Function Documentation

XLALSFTtoRngmed()

int XLALSFTtoRngmed	(	REAL8FrequencySeries *	rngmed,
		const SFTtype *	sft,
		UINT4	blockSize
	)

Calculates a smoothed (running-median) periodogram for the given SFT.

Parameters

[out]	rngmed	running-median smoothed periodo [must be allocated!]
[in]	sft	input SFT
	blockSize	Running median block size

Definition at line 212 of file NormalizeSFTRngMed.c.

XLALSFTtoPeriodogram()

int XLALSFTtoPeriodogram	(	REAL8FrequencySeries *	periodo,
		const COMPLEX8FrequencySeries *	SFT
	)

Calculate the "periodogram" of an SFT, ie the modulus-squares of the SFT-data.

Parameters

[out]	periodo	mod squares of SFT data (has to be allocated)
[in]	SFT	input SFT

Definition at line 260 of file NormalizeSFTRngMed.c.

XLALPeriodoToRngmed()

int XLALPeriodoToRngmed	(	REAL8FrequencySeries *	rngmed,
		const REAL8FrequencySeries *	periodo,
		UINT4	blockSize
	)

Calculates running median over a single periodogram.

Parameters

[out]	rngmed	resulting 'smoothed' periodogram (must be allocated)
[in]	periodo	input periodogram
	blockSize	Running median block size

Definition at line 303 of file NormalizeSFTRngMed.c.

XLALNormalizeSFT()

int XLALNormalizeSFT	(	REAL8FrequencySeries *	rngmed,
		SFTtype *	sft,
		UINT4	blockSize,
		const REAL8	assumeSqrtS
	)

Normalize an sft based on RngMed estimated PSD, and returns running-median.

Parameters

[out]	rngmed	rng-median smoothed periodogram over SFT (Tsft*Sn/2) (must be allocated)
	sft	SFT to be normalized
	blockSize	Running median block size for rngmed calculation
	assumeSqrtS	If >0, instead assume sqrt(S) value *instead* of calculating PSD from running median

Definition at line 68 of file NormalizeSFTRngMed.c.

XLALNormalizeSFTVect()

int XLALNormalizeSFTVect	(	SFTVector *	sftVect,
		UINT4	blockSize,
		const REAL8	assumeSqrtS
	)

Function for normalizing a vector of SFTs.

Parameters

sftVect	[in/out] pointer to a vector of SFTs which will be normalized
blockSize	Running median window size
assumeSqrtS	If >0, instead assume sqrt(S) value *instead* of calculating PSD from running median

Definition at line 120 of file NormalizeSFTRngMed.c.

XLALNormalizeMultiSFTVect()

MultiPSDVector* XLALNormalizeMultiSFTVect	(	MultiSFTVector *	multsft,
		UINT4	blockSize,
		const MultiNoiseFloor *	assumeSqrtSX
	)

Function for normalizing a multi vector of SFTs in a multi IFO search and returns the running-median estimates of the power.

Parameters

multsft	[in/out] multi-vector of SFTs which will be normalized
blockSize	Running median window size
assumeSqrtSX	If !NULL, instead assume sqrt(S^X) values *instead* of calculating PSD from running median

Definition at line 159 of file NormalizeSFTRngMed.c.

XLALSFTstoCrossPeriodogram()

int XLALSFTstoCrossPeriodogram	(	REAL8FrequencySeries *	periodo,
		const COMPLEX8FrequencySeries *	sft1,
		const COMPLEX8FrequencySeries *	sft2
	)

Calculate the cross-correlation periodogram from 2 SFTs.

Parameters

[out]	periodo	modulus square of SFT data (must be allocated)
[in]	sft1	pointer to first SFT
[in]	sft2	pointer to second SFT

Definition at line 368 of file NormalizeSFTRngMed.c.