Audio signal separation through complex tensor factorization: Utilizing modulation frequency and phase information

I propose a complex-valued tensor factorization algorithm for audio-source separation to exploit not only amplitude but phase information of audio signals in the modulation frequency (MF) domain. The proposed algorithm is extended from complex non-negative matrix factorization, which is capable of decomposing an arbitrary complex matrix such as the complex spectrum in the acoustic frequency domain. The proposed method enables us to factorize an arbitrary complex tensor of order 3. The detailed performance of the proposed algorithm for single-channel source separation is investigated through numerical experiments. I examine the quantitative contributions of the MF domain and phase information examined by additionally presenting three tensor factorization algorithms and using five objective indices for source separation.