A Three Dimensional FFT Based Search Scheme for Gravitational Waves from Binary Neutron Star Systems

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Abstract:: Gravitational waves (GW) from binary neutron stars are phase modulated due to a Doppler shift caused by the orbital motion of the stars. This phase modulated signal has an oscillating frequency. Finding the carrier frequency of a phase-modulated signal after applying the Fourier transform is non-trivial. This is due to the modulation factor of the signal, which induces sidebands that vary in magnitude relative to the carrier frequency depending on the size of the modulation index (the extent of the Doppler shift). A GW signal can be extracted from noise using a data search over three parameters: the carrier frequency (ranging from 10-1500 Hz), the modulation frequency (about 0.00001-1 Hz), and the modulation index/amplitude (0-10,000). Key strategies for this search include isolating the modulation factor from the signal and approximating it using the Jacobi-Anger expansion, working in the frequency domain (taking the Fourier Transform only once in the initial step), and utilizing the Convolution Theorem. The program for this search, written in MATLAB, has been able to determine all three parameters from simulated data both with and without noise, though with some limitations that depend on the number of terms used in the Jacobi-Anger expansion and the amount of noise. There are also variations of signals that remain to be addressed.

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LIGO Document T1500307-v2