Equivalence between Frequency-Domain Blind Source Separation and Frequency-Domain Adaptive Beamforming for Convolutive M
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Equivalence between Frequency-Domain Blind Source Separation and Frequency-Domain Adaptive Beamforming for Convolutive Mixtures Shoko Araki NTT Communication Science Laboratories, NTT Corporation, 2-4 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0237, Japan Email: [email protected]
Shoji Makino NTT Communication Science Laboratories, NTT Corporation, 2-4 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0237, Japan Email: [email protected]
Yoichi Hinamoto Graduate School of Information Science, Nara Institute of Science and Technology, 8916-5 Takayama-cho, Ikoma, Nara 630-0192, Japan Email: [email protected]
Ryo Mukai NTT Communication Science Laboratories, NTT Corporation, 2-4 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0237, Japan Email: [email protected]
Tsuyoki Nishikawa Graduate School of Information Science, Nara Institute of Science and Technology, 8916-5 Takayama-cho, Ikoma, Nara 630-0192, Japan Email: [email protected]
Hiroshi Saruwatari Graduate School of Information Science, Nara Institute of Science and Technology, 8916-5 Takayama-cho, Ikoma, Nara, 630-0192, Japan Email: [email protected] Received 2 December 2002 and in revised form 16 March 2003 Frequency-domain blind source separation (BSS) is shown to be equivalent to two sets of frequency-domain adaptive beamformers (ABFs) under certain conditions. The zero search of the off-diagonal components in the BSS update equation can be viewed as the minimization of the mean square error in the ABFs. The unmixing matrix of the BSS and the filter coefficients of the ABFs converge to the same solution if the two source signals are ideally independent. If they are dependent, this results in a bias for the correct unmixing filter coefficients. Therefore, the performance of the BSS is limited to that of the ABF if the ABF can use exact geometric information. This understanding gives an interpretation of BSS from a physical point of view. Keywords and phrases: blind source separation, convolutive mixtures, adaptive beamformers.
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INTRODUCTION
Blind source separation (BSS) is an approach for estimating source signals si (t) using only the information on mixed signals x j (t) observed at each input channel. BSS can be applied to achieve noise-robust speech recognition and high-quality
hands-free telecommunication. It might also become one of the cues for auditory scene analysis. Several methods have been proposed for BSS of convolutive mixtures [1, 2]. Some approaches consider the impulse responses of a room h ji as FIR filters, and estimate those filters in the time domain [3, 4, 5]; other approaches
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EURASIP Journal on Applied Signal Processing
transform the problem into the frequency domain to solve an instantaneous BSS problem for every frequency simultaneously [6, 7]. Here, we consider the BSS of convolutive mixtures of speech in the frequency domain. In this paper, we provide an interpretation of BSS from a physical point of view showing the equivalence between frequency-domain BSS and two sets of frequ
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