A sparse periodic decomposition and its application to speech representation

This study proposes a method to decompose a signal into a set of periodic signals with time-varying amplitude. The proposed method imposes a penalty on the resultant periodic subsignals in order to improve the sparsity of the decomposition. This penalty is defined as the sum of the l2 norms of the resultant periodic subsignals to find the shortest path to the approximation. By this penalty of the sparsity, the proposed decomposition extracts significant periodic components from a mixture and has ability of the source estimation for mixtures of periodic signals. In experiments, we apply the proposed decomposition to speech mixtures and demonstrate that the proposed decomposition can estimate periodic components of each source speech and detects pitch contours of the source. In additionally, the single-channel speech separation using a lazy assignment of the periodic signals is presented to demonstrate the source separation capability of the proposed decomposition.