Previous work relevant to the current system falls into two general categories: nonstationary sinusoidal modeling parameter estimation and Fresnel analysis. The author included a review of the former in [3]. To summarize, previous work has focused on better matching sinusoidal trajectories across frames, rather than on trying to get better data at the frame level. The author's work ([3]), however, used a vocoder model at the frame level to better parameterize so-called smeared spectral peaks that tend to indicate nonstationary quasi-sinusoidal signals. In the process of creating the system presented therein, the author discovered that for practical speech and audio signals, the frequency trajectories were in general slowly varying enough to be well-modeled as linear. That observation is a motivating factor for the current system, which, in application, implicitly assumes that this is true.
Recent work by Liu [2] has investigated linear frequency chirps in continuous time, and has included a closed form expression for the frequency slope parameter as a function of the Fourier transform and its second derivative. This model, however, is more sensitive to noise than the currently proposed models, and loses accuracy for signals whose frequency changes only slowly. Modifications to Liu's model are being researched by the author.