Frequency domain exploits for symmetric adaptive decorrelation : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Engineering at Massey University, Albany, New Zealand

Abstract

Symmetric adaptive decorrelation (SAD) is a semi-blind method of separating convolutely mixed signals. While it has restrictions on the physical layout of the demixing equipment, restrictions not present for many other blind source separation (BSS) techniques, it is more ideally suited for some applications (for example, live sound mixing) due to the fact that no post-processing is required to ascertain which output corresponds with which source. Since the SAD algorithm is based on second-order statistics (SOS), it also tends to have a lower computational load when compared with those based on higher order statistics. In order to increase the e ciency of the SAD algorithm, a multibranched recursive structure is investigated. While a nominal gain in e ciency is attained, we move away from this approach in pursuit of more substantial gains. A frequency-domain symmetric adaptive decorrelation (FD-SAD) algorithm is proposed, with savings increasing not only with larger lter sizes, but also with increasing the number of sources. The convergence and stability of this new algorithm is proven. A trade-o of the FD-SAD algorithm is that it introduces a delay in the output, which renders the algorithm unsuitable for real-time applications. Therefore a hybrid approach is also proposed that does not su er from the lag of the frequency domain approach. While the proposed algorithm is slightly less computationally e cient than the pure frequency domain algorithm, it is signi cantly more e cient than the time-domain approach. A comparison of the frequency domain and hybrid algorithms shows that both achieve separation equivalent to the time-domain algorithm in a real-world environment. The proposed adaptations could also be used to extend other BSS approaches (such as Triple-N ICA for Convolutive mixtures (TRINICON) [1], which can also be based on SOS), and a comparison of the proposed methods with TRINICON is explored.