  We demonstrate a method to extend the range of pulsed laser spin noise
measurements to long spin lifetimes. We use an analog time-domain detection
scheme with a bandwidth limited only by laser pulse duration. Our model uses
statistics and Bloch-Torrey equations to extract the Lande g-factor, Faraday
cross-section $\sigma_F$, and spin lifetime $\tau_S$, while accounting for
finite detector response. Varying the magnetic field with a fixed probe-probe
delay yields $\tau_S$ when it is longer than the laser repetition period.
Varying the probe-probe delay with a fixed field produces a time-domain
measurement of the correlation function.
