Signal analysis of the gravitational waveform of pulsars

Abstract

We present signal analysis for the detection of gravitational radiation from pulsars. Typically the observation times will be of the order of a few weeks or months. Due to the rotation and orbital motion of the Earth, a monochromatic signal gets frequency and amplitude modulated. The effect of both these modulations is to smear out the monochromatic signal into a small bandwidth about the signal frequency of the wave. However, the effect on the Fourier transform of frequency modulation is much more severe compared to amplitude modulation in that the height of the peak is reduced drastically. The spread in the frequency, Δf ≈ 2πf₀R/c , where f₀ is the frequency of the signal, R the radius of the Earth and c the velocity of light. Further, we develop analytical approximations to Fourier transform of the pulsar taking into account the rotation of the Earth and then the orbital correction to the signal. lnspection of the expression shows that for a 1kHz signal and one day observation time, the signal is spread into about 100 bands. These calculations are performed for arbitrary orientations of the detector and the arbitrary wave parameters.