A Sparse Decomposition for Periodic Signal Mixtures
Makoto Nakashizuka · 2007
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 thel2norms 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.