The propagation of a thermal-neutron pulse through homogeneous neutronic systems, multiplying or non-multiplying, is studied with the aid of the general linear model. This model is characterized by a complex dispersion law that governs the neutron-wave optics of the system. The dispersion of the pulse, which may be regarded as a superposition of a continuous spectrum of monochromatic waves, is also governed by the system dispersion law. It is shown that Fourier transformed moments of the pulse, evaluated at a sequence of detector positions within the system, yield derivatives of the dispersion law. The order of the derivative is just the order of the moment. In zero'th order, one reverts to the conventional neutron-wave experiment. Using this method of analysis, a thermal-pulse experiment, in principle, can be made to yield more information than can a wave experiment and could serve as the basis of an on-line monitor of power reactor stability.