Spectral Analysis of Analytic Signal

摘要

In this article, we study the spectral distribution of a kind of special matrix which originates from the dictionary of Cauchy kernels. This research is a part of our reconstructions of analytic signals. The numerical advantage of this result for sparse reconstruction lies in the fact that the singular values decay fast since the largest eigenvalue takes a overwhelming portion of the trace. We also give two numerical illustration and Python codes for this estimation.