A convenient formalism is developed that allows one to express the transmission coefficient of a wave propagating in a one-dimensional disordered structure through the determinant T_N= mod D_N mod ^-2, which depends on the amplitudes of reflection of a single scatterer only. It is shown that the density of states averaged over the sample as well as the spectrum of surface and volume waves in such a layered system may also be represented by the determinant D_N.