StackMetric.h File Reference

Author:: Creighton, T.Provides routines to compute parameter-space metrics for coherent or stacked pulsar searches.

#include <lal/LALStdlib.h>
#include <lal/PulsarTimes.h>

Include dependency graph for StackMetric.h:

Go to the source code of this file.

Data Structures

struct tagMetricParamStruc

This structure stores and passes parameters for computing a parameter-space metric. More...

Defines

Error conditions

#define STACKMETRICH_ENUL   1

#define STACKMETRICH_EBAD   2

#define STACKMETRICH_MSGENUL   "Null pointer"

#define STACKMETRICH_MSGEBAD   "Bad parameter values"

Typedefs

typedef tagMetricParamStruc MetricParamStruc

This structure stores and passes parameters for computing a parameter-space metric.

Functions

NRCSID (STACKMETRICH,"$Id: StackMetric.h,v 1.11 2007/06/08 14:41:50 bema Exp $")

void LALCoherentMetric (LALStatus *, REAL8Vector *metric, REAL8Vector *lambda, MetricParamStruc *params)

void LALStackMetric (LALStatus *, REAL8Vector *metric, REAL8Vector *lambda, MetricParamStruc *params)

void LALProjectMetric (LALStatus *, REAL8Vector *metric, BOOLEAN errors)

Detailed Description

Author:: Creighton, T.Provides routines to compute parameter-space metrics for coherent or stacked pulsar searches.

Date:: 2000 -- 2003

Id: StackMetric.h,v 1.11 2007/06/08 14:41:50 bema Exp

Description

This header covers routines that determine the metric coefficients for the mismatch function (ambiguity function) on the parameter space for a pulsar search. The assumed search method is stacking one or more Fourier power spectra, after some suitable demodulation.

The method for determining the parameter metric is discussed in detail in Sec.~II of Brady_P2000; we present the key results here in brief. We assume that a model waveform in our search is described by an overall frequency scale $f_0$ , and by some modulation about that frequency described by ``shape'' parameters $\vec{\lambda}=(\lambda^1,\ldots,\lambda^n)$ , such that the parameterized phase of the waveform is $\phi[t;\mathbf{\lambda}] = 2\pi f_0\tau[t;\vec{\lambda}]$ . Here $\mathbf{\lambda} = (\lambda^0,\vec{\lambda}) = (f_0,\lambda^1,\ldots,\lambda^n)$ represents the total set of parameters we must search over, and $\tau[t;\vec{\lambda}]$ is a canonical time coordinate describing the shape of the waveform.

A (local) maximum in detected power $P$ occurs if a signal is filtered (or demodulated in time and the Fourier spectrum is sampled) using a phase model that matches the true phase of the signal. If the parameters $\mathbf{\lambda}$ do not match the true parameters of the signal, then the detected power will be degraded. The fractional power loss $\Delta P/P$ thus has a (local) minimum of 0 for matched parameters and increases for mismatched parameters; it can be thought of as describing a distance between the two (nearby) parameter sets. The metric of this distance measure is simply the set of quadratic coefficients of the Taylor expansion of $\Delta P/P$ about its minimum.

Clearly the power will degrade rapidly with variation in some parameter $\lambda^\alpha$ if the phase function $\phi$ depends strongly on that parameter. It turns out that if the detected power is computed from a coherent power spectrum of a time interval $\Delta t$ , then the metric components are given simply by the covariances of the phase derivatives $\partial\phi/\partial\lambda^\alpha$ over the time interval:

$\begin{equation} g_{\alpha\beta}(\mathbf{\lambda}) = \left\langle \frac{\partial\phi[t;\mathbf{\lambda}]}{\partial\lambda^\alpha} \frac{\partial\phi[t;\mathbf{\lambda}]}{\partial\lambda^\beta} \right\rangle - \left\langle \frac{\partial\phi[t;\mathbf{\lambda}]}{\partial\lambda^\alpha} \right\rangle \left\langle \frac{\partial\phi[t;\mathbf{\lambda}]}{\partial\lambda^\beta} \right\rangle \; , \end{equation}$

where $\langle\ldots\rangle$ denotes a time average over the interval $\Delta t$ , and $\alpha$ and $\beta$ are indecies running from 0 to $n$ . The partial derivatives are evaluated at the point $\mathbf{\lambda}$ in parameter space. If instead the detected power is computed from the sum of several power spectra computed from separate time intervals (of the same length), then the overall metric is the average of the metrics from each time interval.

When power spectra are computed using fast Fourier transforms, the entire frequency band from DC to Nyquist is computed at once; one then scans all frequencies for significant peaks. In this case one is concerned with how the peak power (maximized over frequency) is reduced by mismatch in the remaining ``shape'' parameters $\vec{\lambda}$ . This is given by the the projected metric $\gamma_{ij}(\vec{\lambda})$ , where $i$ and $j$ run from 1 to $n$ :

$\begin{equation} \gamma_{ij}(\vec{\lambda}) = \left[g_{ij}-\frac{g_{0i}g_{0j}}{g_{00}} \right]_{\lambda^0=f_\mathrm{max}} \; . \end{equation}$

Here $f_\mathrm{max}$ is the highest-frequency signal expected to be present, which ensures that, for lower-frequency signals, $\gamma_{ij}$ will overestimate the detection scheme's sensitivity to the ``shape'' parameters.

Definition in file StackMetric.h.

Define Documentation

#define STACKMETRICH_ENUL 1

Definition at line 123 of file StackMetric.h.

#define STACKMETRICH_EBAD 2

Definition at line 124 of file StackMetric.h.

#define STACKMETRICH_MSGENUL "Null pointer"

Definition at line 126 of file StackMetric.h.

#define STACKMETRICH_MSGEBAD "Bad parameter values"

Definition at line 127 of file StackMetric.h.

Typedef Documentation

typedef struct tagMetricParamStruc MetricParamStruc

This structure stores and passes parameters for computing a parameter-space metric.

It points to the canonical time function used to compute the metric and to the parameters required by this function. In addition, this structure must indicate the timespan over which the timing differences accumulate, and whether this accumulation is coherent or divided into stacks which are summed in power.

Function Documentation

NRCSID	(	STACKMETRICH	,
		"$Id: StackMetric.	h,
		v 1.11 2007/06/08 14:41:50 bema Exp $"
	)

void LALCoherentMetric	(	LALStatus *	,
		REAL8Vector *	metric,
		REAL8Vector *	lambda,
		MetricParamStruc *	params
	)

Definition at line 160 of file CoherentMetric.c.

void LALStackMetric	(	LALStatus *	,
		REAL8Vector *	metric,
		REAL8Vector *	lambda,
		MetricParamStruc *	params
	)

Definition at line 80 of file StackMetric.c.

void LALProjectMetric	(	LALStatus *	,
		REAL8Vector *	metric,
		BOOLEAN	errors
	)

Definition at line 94 of file ProjectMetric.c.

Generated on Sat Sep 6 03:08:31 2008 for LAL by

1.5.2


Data Structures
struct	tagMetricParamStruc
	This structure stores and passes parameters for computing a parameter-space metric. More...
Defines
Error conditions
#define	STACKMETRICH_ENUL 1
#define	STACKMETRICH_EBAD 2
#define	STACKMETRICH_MSGENUL "Null pointer"
#define	STACKMETRICH_MSGEBAD "Bad parameter values"
Typedefs
typedef tagMetricParamStruc	MetricParamStruc
	This structure stores and passes parameters for computing a parameter-space metric.
Functions
	NRCSID (STACKMETRICH,"$Id: StackMetric.h,v 1.11 2007/06/08 14:41:50 bema Exp $")
void	LALCoherentMetric (LALStatus , REAL8Vector metric, REAL8Vector lambda, MetricParamStruc params)
void	LALStackMetric (LALStatus , REAL8Vector metric, REAL8Vector lambda, MetricParamStruc params)
void	LALProjectMetric (LALStatus , REAL8Vector metric, BOOLEAN errors)