On the Design and Use of Once-differentiable High Dynamic Resolution Atoms for the Distribution Derivative Method
The accuracy of the Distribution Derivative Method (DDM)  is evaluated on mixtures of chirp signals. It is shown that accurate estimation can be obtained when the sets of atoms for which the inner product is large are disjoint. This amounts to designing atoms with windows whose Fourier transform exhibits low sidelobes but which are once-differentiable in the time-domain. A technique for designing once-differentiable approximations to windows is presented and the accuracy of these windows in estimating the parameters of sinusoidal chirps in mixture is evaluated.