Mathematical view of a blind source separation on a time frequency space

To treat the blind source separation problems, in many cases, either statistical independence or statistical orthogonality (uncorrelation) on the sources has been assumed. Napoletani–Berenstein–Krishnaprasad treated the problem under the linear independence of the windowed Fourier transforms of sources and the continuity of density functions defined statistically. In this paper, another independence of the windowed Fourier transforms of sources in a time–frequency domain is proposed without assuming any statistical conditions. This paper is a summary of the authors’ submitted papers.