Convolutive blind source separation for more than two sources in the frequency domain

Blind source separation (BSS) for convolutive mixtures can be efficiently achieved in the frequency domain, where independent component analysis is performed separately in each frequency bin. However, frequency-domain BSS involves a permutation problem, which is well known as a difficult problem, especially when the number of sources is large. This paper presents a method for solving the permutation problem, which works well even for many sources. The successful solution for the permutation problem highlights another problem with frequency-domain BSS that arises from the circularity of the discrete frequency representation. This paper discusses the phenomena of the problem and presents a method for solving it. With these two methods, we can separate many sources with a practical execution time. Moreover, real-time processing is currently possible for up to three sources with our implementation.