The Hough Transform

Detailed Description

This package provides routines which implement the Hough-transform as a search-method for unknown pulsars.

Routines implementing the Hough-transform as a search-method for unknown pulsars.

Author

Alicia M. Sintes, M. Alessandra Papa., Krishnan, B.

The hierarchical Hough transform search strategy is an efficient and highly parallel computer algorithm [24] , [18] . This package provides the necessary routines for the Hough incoherent search (the second stage of the search) to track the frequency evolution of peaks in the spectra, which is known in advance for some choice of the source parameters.

The Hough transform is a transformation between the data and the space of parameters that describe the signal.

Input:

Set of points in time-frequency plane that have been obtained from the demodulated FT. The demodulation has been performed with respect to a certain sky location and certain spin-down parameters, in such a way that, if a source was located in the center of the patch and having the same spin-down parameters for which it has been demodulated, we will observe a set of points forming a horizontal line at the intrinsic frequency of the source \(f_0\). Due to the mismatch between the source parameters and the demodulated parameters we will observe a certain pattern in the time frequency diagram following theHough transform master equation.

Output:

Histograms in the parameter space: for each \(f_0\), residual spin-down and refined sky location.

The principle is the following: for every point in the time-frequency plane, we enhance the number count in the histogram in the pixels that are consistent. At the end of this procedure, significant clustering in a pixel in parameter space indicates likelihood of the data containing a signal having the parameters of that pixel.

The package is organized under the modules Header LUT.h, Header PHMD.h, Header HoughMap.h, Header LALHough.h and the files PatchGrid.c, Stereographic.c, ParamPLUT.c, NDParamPLUT.c, ConstructPLUT.c, Peak2PHMD.c, HoughMap.c, and DriveHough.c.

Acknowledgment:

The authors thank S. Frasca and C. Palomba for helpful discussions, F. Massaioli for helping in the initial stages of code development, and B. Allen and J. Creighton for their valuable implementation advice.

Modules
	Header HoughMap.h
	Provides subroutines for initialization and construction of Hough-map derivatives and total Hough-maps.
	Header LALHough.h
	Routines for building and updating the space of partial Hough map derivatives and related functions needed for the construction of total Hough maps at different frequencies and possible residual spin down parameters.
	Header LUT.h
	Provides structures and function prototypes required for the construction of look up tables that are the core for building the Hough maps.
	Header PHMD.h
	Conversion from peaks in a spectrum into a partial Hough map derivative.
	Statistics
	Computes statistics of the Hough maps.
	Header Velocity.h
	Computation of instant and averaged velocities for a given detector and the like.