  We search for the signature of an isotropic stochastic gravitational-wave
background in pulsar timing observations using a frequency-domain correlation
technique. These observations, which span roughly 12 yr, were obtained with the
64-m Parkes radio telescope augmented by public domain observations from the
Arecibo Observatory. A wide range of signal processing issues unique to pulsar
timing and not previously presented in the literature are discussed. These
include the effects of quadratic removal, irregular sampling, and variable
errors which exacerbate the spectral leakage inherent in estimating the steep
red spectrum of the gravitational-wave background. These observations are found
to be consistent with the null hypothesis, that no gravitational-wave
background is present, with 76 percent confidence. We show that the detection
statistic is dominated by the contributions of only a few pulsars because of
the inhomogeneity of this data set. The issues of detecting the signature of a
gravitational-wave background with future observations are discussed.
