Linear signal theory analysis has been applied to the problem of finding the time of flight spectra of random and pseudo-random particle fluxes. The results indicate that by employing the methods of correlation detection with suitable particle detectors, significant improvement in the time resolution in some cases and elimination of the pile-up problems of standard particle-by-particle TOF spectroscopy techniques can be achieved. Two different systems based on using correlation detection have been proposed for use with the time coherent LAMPF accelerator beams. One of these, a high speed camera, has been tested at LAMPF. The results of this test are presented. The second system, a method utilizing RF technology, has not been tested.