It has been known that the linear predictor coefficients (LPC) of speech signals can be transformed into a “pseudo” vocal-tract area function whose boundary conditions are (a) a complete opening at the lips and (b) a matching resistance termination at the glottis. If the boundary condition at the glottis is replaced by a complete opening or a complete closure, all the poles of the resulting system function will move onto the unit circle in z plane. Using this fact it is possible to describe the original LPCs by two sets of pole frequencies corresponding to the two new boundary conditions at the glottis, or a set of frequency-residue pairs corresponding to either set of poles. These representations have several important features: (1) If an original pole is narrow band, the new pole is close to the original pole; (2) the two sets of pole frequencies alternate and are ordered on the frequency axis; and (3) the problem of locating complex poles can be reduced to solving a polynomial with real roots whose order is one-half that of the original all-pole transfer function.
We describe a new method of blind source separation (BSS) on a microphone array combining subband independent component analysis (ICA) and beamforming. The proposed array system consists of the following three sections: (1) subband ICA-based BSS section with estimation of the direction of arrival (DOA) of the sound source, (2) null beamforming section based on the estimated DOA, and (3) integration of (1) and (2) based on the algorithm diversity. Using this technique, we can resolve the low-convergence problem through optimization in ICA. To evaluate its effectiveness, signal-separation and speech-recognition experiments are performed under various reverberant conditions. The results of the signal-separation experiments reveal that the noise reduction rate (NRR) of about 18 dB is obtained under the nonreverberant condition, and NRRs of 8 dB and 6 dB are obtained in the case that the reverberation times are 150 milliseconds and 300 milliseconds. These performances are superior to those of both simple ICA-based BSS and simple beamforming method. Also, from the speech-recognition experiments, it is evident that the performance of the proposed method in terms of the word recognition rates is superior to those of the conventional ICA-based BSS method under all reverberant conditions
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