In this paper, we introduce a sparse recovery strategy for analytic signals in Hardy space H(D), where D denotes the unit disk of the complex plane. The representation strategy is based on the optimization technique. We investigate the asymptotic singular values distribution of the dictionary matrix and give an estimation of the number of rows of the random matrix. To the best of our knowledge, this is the first time that such result is given. This result demonstrates that the dictionary of the normalized Szegö kernels (or reproducing kernels) is perfect for decompositions of analytic signals. A numerical example is presented exhibiting the theory. As applications, we still work on time-frequency analysis and propose a new type of non-negative time-frequency distribution associated with mono-components in the periodic case.