  In this paper, we propose a new framework for treating the angular
information in the pulsar timing array response to a gravitational wave
background based on standard cosmic microwave background techniques. We
calculate the angular power spectrum of the all-sky gravitational redshift
pattern induced at the earth for both a single bright source of gravitational
radiation and a statistically isotropic, unpolarized Gaussian random
gravitational wave background. The angular power spectrum is the harmonic
transform of the Hellings & Downs curve. We use the power spectrum to examine
the expected variance in the Hellings & Downs curve in both cases. Finally, we
discuss the extent to which pulsar timing arrays are sensitive to the angular
power spectrum and find that the power spectrum sensitivity is dominated by the
quadrupole anisotropy of the gravitational redshift map.
