A novel parametrically efficient approach to estimating the spectra of short transient signals is proposed and evaluated, with an application to estimating material properties, including complex refractive index and absorption coefficient, in the terahertz frequency range. This technique includes uncertainty analysis of the obtained spectral estimates, allowing rigorous statistical comparison between samples. In the proposed approach, a simple few-parameter continuous-time transfer function model explains over 99.9% of the measured signal. The problem, normally solved using poorly numerically defined Fourier transform deconvolution methods, is reformulated and cast as a time-domain dynamic-system estimation problem, thus providing a true time-domain spectroscopy tool.