  We investigate the use of harmonic analysis techniques to perform
measurements of the angular power spectrum on mock pulsar timing data for an
isotropic stochastic gravitational-wave background (SGWB) with a dimensionless
strain amplitude $A_{\text{gw}}=2 \times 10^{-15}$ and spectral index
$\gamma_{\text{gw}}=13/3$. We examine the sensitivity of our harmonic analysis
to the number of pulsars (50, 100, and 150) and length of pulsar observation
time (10, 20, and 30 years) for an isotropic distribution of pulsars. We
account for intrinsic pulsar red noise and use an average value of white noise
of ~100 ns. We are able to detect the quadrupole for all our mock harmonic
analyses, and for the analysis with 150 pulsars observed for 30 years, we are
able to detect up to the $\ell = 5$ multipole. We provide scaling laws for the
SGWB amplitude, the quadrupole, and $\ell = 3$ as a function of pulsar
observation time and as a function of number of pulsars. We estimate the
sensitivity of our harmonic approach to deviations of General Relativity that
produce subluminal gravitational wave propagation speeds.
