  We investigate the computational requirements for all-sky, all-frequency
searches for gravitational waves from spinning neutron stars, using archived
data from interferometric gravitational wave detectors such as LIGO. These
sources are expected to be weak, so the optimal strategy involves coherent
accumulaton of signal-to-noise using Fourier transforms of long stretches of
data (months to years). Earth-motion-induced Doppler shifts, and intrinsic
pulsar spindown, will reduce the narrow-band signal-to-noise by spreading power
across many frequency bins; therefore, it is necessary to correct for these
effects before performing the Fourier transform. The corrections can be
implemented by a parametrized model, in which one does a search over a discrete
set of parameter values. We define a metric on this parameter space, which can
be used to determine the optimal spacing between points in a search; the metric
is used to compute the number of independent parameter-space points Np that
must be searched, as a function of observation time T. The number Np(T) depends
on the maximum gravitational wave frequency and the minimum spindown age
tau=f/(df/dt) that the search can detect. The signal-to-noise ratio required,
in order to have 99% confidence of a detection, also depends on Np(T). We find
that for an all-sky, all-frequency search lasting T=10^7 s, this detection
threshhold is at a level of 4 to 5 times h(3/yr), where h(3/yr) is the
corresponding 99% confidence threshhold if one knows in advance the pulsar
position and spin period.
