A study of the gravitational wave form from pulsars

Abstract

We present a study of the gravitational wave form from pulsars. Typically the observation times will be of the order of a few months. Due to the rotation and orbital motion of the Earth, a monochromatic signal becomes 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 the frequency modulation is much more severe compared to the amplitude modulation in that the height of the peak is reduced drastically. The Fourier transform of the pulsar signal, taking into account the rotation of the Earth for one day observation period is studied. We have obtained an analytical closed form of the Fourier transform considering the rotational motion of the Earth only. With the inclusion of orbital corrections one obtains a double series of Bessel functions.