Abstract

The direct detection of continuous gravitational waves from pulsars is a much anticipated discovery in the emerging field of multimessenger gravitational wave (GW) astronomy. Because putative pulsar signals are exceedingly weak large amounts of data need to be integrated to achieve desired sensitivity. Contemporary searches use ingenious ad hoc methods to reduce computational complexity. In this paper we provide analytical expressions for the Fourier transform of realistic pulsar signals. This provides description of the manifold of pulsar signals in the Fourier domain, used by many search methods. We analyze the shape of the Fourier transform and provide explicit formulas for location and size of peaks resulting from stationary frequencies. We apply our formulas to analysis of recently identified outlier at 1891.76 Hz.

Highlights

  • Continuous gravitational waves are an eagerly anticipated but elusive phenomena [1]

  • In this paper we provide analytical expressions for the Fourier transform of realistic pulsar signals

  • We analyze the shape of the Fourier transform and provide explicit formulas for location and size of peaks resulting from stationary frequencies

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Summary

INTRODUCTION

Continuous gravitational waves are an eagerly anticipated but elusive phenomena [1]. Despite a series of searches since early 2000 (in particular [2,3,4,5,6,7,8]) there have been no loud detections. The Fourier transform of continuous wave signal is analogous to the time-domain representation of a binary waveform Understanding it is essential for interpreting detection candidates. Our analytical results yield a simple method for determining location and strengths of peaks in the Fourier transform of a continuous wave signal, without the need to generate the entire waveform. This has immediate applications for understanding the influence of detector artifacts. We provide explicit formulas describing location and strength of the peaks in the Fourier transform These formulas can be used to efficiently solve both direct and inverse problems of correspondence between signals and sharp detector artifacts.

SIGNAL MODEL
Signal spectrum
Polynomial approximation
Jacobi-Anger expansion
FOURIER TRANSFORM SHAPE
SPECTRUM SHAPE ALGORITHM
PERFORMANCE
VIII. CONCLUSIONS

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