LALInspiralWaveNormaliseLSO.c File Reference

Module to find the norm of a signal and to return a normaliseLSOd array. The original signal is left untouched. More...

Prototypes
void	LALInspiralWaveNormaliseLSO (LALStatus *status, REAL4Vector *filter, REAL8 *norm, InspiralWaveNormaliseIn *in)

Detailed Description

Module to find the norm of a signal and to return a normaliseLSOd array. The original signal is left untouched.

Author

Sathyaprakash, B. S.

Prototypes

LALInspiralWaveNormaliseLSO()

Description

Given the positive frequency Fourier components \(H_k,\) \(k=0,\ldots,n-1,\) of a vector and the noise PSD \(S_m,\) \(m=0,\ldots,n/2,\) this module first computes the norm \(H\) of the vector treating \(S_m\) as the measure: (note that in {fftw} notation, the zeroth frequency component is \(H_0,\) Nyquist is \(H_{n/2},\) \(H_k,\) \(k \ne 0,n/2,\) ( \(H_{n-k})\) is the real (imaginary) part of the \(k\)th harmonic)

\begin{equation} \label{eq_inspiralnorm} H = \sum_{k=1}^{n/2-1} \frac{H_k^2 + H^2_{n-k}}{S_k}. \end{equation}

The above sum is limited to frequency in->fCutoff. Also, note that the zeroth and Nyquist frequency components are ignored in the computation of the norm. Moreover, array elements of filter corresponding to frequencies greater than in->fCutoff are set to zero. That is, the code replaces the original vector \(H_k\) with normalized vector using:

\begin{eqnarray} \widehat H_k & = & \frac {H_k}{\sqrt H}, \ \ \ \mathrm{k \times in\rightarrow\mathrm df} \le \mathrm{in\rightarrow fCutoff}, \\ & = & 0, \ \ \ \mathrm{k \times in\rightarrow df} > \mathrm{in\rightarrow fCutoff}. \end{eqnarray}

In addition, the 0th and Nyquist frequency components are also set to zero.

Algorithm

Uses

none.

Notes

Definition in file LALInspiralWaveNormaliseLSO.c.

Go to the source code of this file.

Function Documentation

LALInspiralWaveNormaliseLSO()

void LALInspiralWaveNormaliseLSO	(	LALStatus *	status,
		REAL4Vector *	filter,
		REAL8 *	norm,
		InspiralWaveNormaliseIn *	in
	)

Definition at line 76 of file LALInspiralWaveNormaliseLSO.c.