(1) where (k) is the impulse response from source to microphone. The method i-th m-th proposed in this paper is applicable to the underdetermined case where the sources outnumber the sensors, namely N>M. In the time-frequency domain by transformed by STFT (Short-Time Fourier Transform) the mixed observations of (1) is represented (2) where are the STFT’s of respectively, is the DFT of , is the index of discrete , l frequency bin, is the time-frame index. Let (m=1, denote the location of the k …, M) sensor in 3-D space, and assume the first sensor is located at the origin () without m-th loss of generality. A source direction vector referred to as the Time Delay and Phase Difference: propagation direction vector is defined by (3) where denotes the azimuth angle of source direction, , and constitutes a unit sphere. An acoustic signal with a propagation direction vector induces time delays of arrival between sensor and the or the reference sensor as follows. m-th (4) where c is the travelling speed. The vector-matrix formulation of above is represented by (5) where Define the following difference vector from the observations. (6) , then from (5) we have the following relationship (7) where is sampling frequency. Difference Let’s define a mapping and propagation vector: R : (8) , in specific, R can be represented by R (9) The inverse operation of R, that is R-1 : (10) can be obtained by our previous method proposed in [9], by exploiting Gram-Schmidt orthogonalization in -space. In real observations, due to multiple sources interaction, Reliable T-F cell selection:
(1) where (k) is the impulse response from i-th source to m-th microphone. The method proposed in this paper is applicable to the underdetermined case where the sources outnumber the sensors, namely N>M. In the time-frequency domain by transformed by STFT (Short-Time Fourier Transform) the mixed observations of (1) is represented (2) where are the STFT’s of , respectively, is the DFT of , l is the index of discrete frequency bin, k is the time-frame index. Let (m=1, …, M) denote the location of the m-th sensor in 3-D space, and assume the first sensor is located at the origin () without loss of generality. Time Delay and Phase Difference: A source direction vector referred to as the propagation direction vector is defined by (3) where denotes the azimuth angle of source direction, , and constitutes a unit sphere. An acoustic signal with a propagation direction vector induces time delays of arrival between m-th sensor and the or the reference sensor as follows. (4) where c is the travelling speed. The vector-matrix formulation of above is represented by (5) where Define the following difference vector from the observations. (6) , then from (5) we have the following relationship (7) where is sampling frequency. Difference and propagation vector: Let’s define a mapping R : (8) , in specific, R can be represented by R (9) The inverse operation of R, that is R-1 : (10) can be obtained by our previous method proposed in [9], by exploiting Gram-Schmidt orthogonalization in -space. Reliable T-F cell selection: In real observations, due to multiple sources interaction,
RiTA2012-final-paper.docx