In this work we present analytic and numerical treatments of the
gravitational wave signal from a pulsar which includes spindown. We consider
phase corrections to a received monochromatic signal due to rotational and
elliptical orbital motion of the Earth, as well as perturbations due to Jupiter
and the Moon. We discuss the Fourier transform of such a signal, which is
expressed in terms of well known special functions and lends itself to a
tractable numerical analysis.