Estimation of chirp signals with time-varying amplitudes

The problem of parameters estimation of signals composed of an unknown number of chirps with time-varying amplitude is presented using a sparse reconstruction framework. The method employs a parametric model using a weighted combination of splines to model the time-varying nature of the signal amplitudes. To obtain high-resolution of the frequencies and to avoid large dimensional matrices, a dictionary refinement technique is employed. The method can accurately estimate the amplitude and frequency parameters of multiple signal components, and may be extended to allow for non-linear chirps. Furthermore, an efficient implementation to solve the resulting optimization problem is proposed. Results on both synthetic and experimental signals illustrate the efficient performance of the algorithm.