Compressed sensing is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. Compressed sensing has demonstrated that data acquisition and compression can often be combined, dramatically reducing the time and space needed to acquire many signals of interest. Despite the tremendous impact of compressed sensing on signal processing theory and practice, its development thus far has focused on signals with sparse representations in finite discrete dictionaries. In this project, the system address the problem of simultaneously recovering a joint frequency-sparse (JFS) signal ensemble sharing a common frequency-sparse component, with frequencies continuously. This common/innovation joint sparsity model is shown to significantly reduce the number of measurements in conventional distributed CS framework by utilizing common information shared in multiple signals. This system is mainly to develop the continuous counterpart of the joint sparsity model. And it proposes the concatenated atomic norm for the description of joint frequency sparsity of which the minimization can be solved via SDP. The system characterize a dual certificate for the optimality of the proposed optimization problem.