A Sparse Decomposition for Periodic Signal Mixtures

This study proposes a method to decompose a signal into a set of periodic signals. The proposed decomposition method imposes a penalty on the resultant periodic subsignals in order to improve the sparsity of decomposition and avoid the over-estimation of periods. This penalty is defined as the weighted sum of the l ₂ norms of the resultant periodic subsignals. This decomposition is approximated by an unconstrained minimization problem. In order to solve this problem, a relaxation algorithm is applied. In the experiments, decomposition results are presented to demonstrate the simultaneous detection of periods and waveforms hidden in signal mixtures. In additionally, the decomposition of a speech mixture is also demonstrated.