TY - GEN

T1 - Space-time coherence and its exact null distribution

AU - Klausner, Nick

AU - Azimi-Sadjadi, Mahmood

AU - Scharf, Louis

AU - Cochran, Douglas

PY - 2013/10/18

Y1 - 2013/10/18

N2 - This paper considers the problem of testing for the independence among multiple (≥ 2) random vectors with each random vector representing a time series captured at one sensor. Implementing the Generalized Likelihood Ratio Test involves testing the null hypothesis that the composite covariance matrix of the channels is block-diagonal through the use of a generalized Hadamard ratio. Using the theory of linear prediction and its connection with Gram determinants, it is shown that this generalized Hadamard ratio can be written as a product of scalars which are independently drawn from a beta distribution under the null hypothesis. This result is useful from a Monte Carlo analysis standpoint in that it is much more computationally efficient to form a product of scalar beta random variables than it is to compute the determinant of complex Wishart matrices.

AB - This paper considers the problem of testing for the independence among multiple (≥ 2) random vectors with each random vector representing a time series captured at one sensor. Implementing the Generalized Likelihood Ratio Test involves testing the null hypothesis that the composite covariance matrix of the channels is block-diagonal through the use of a generalized Hadamard ratio. Using the theory of linear prediction and its connection with Gram determinants, it is shown that this generalized Hadamard ratio can be written as a product of scalars which are independently drawn from a beta distribution under the null hypothesis. This result is useful from a Monte Carlo analysis standpoint in that it is much more computationally efficient to form a product of scalar beta random variables than it is to compute the determinant of complex Wishart matrices.

KW - Generalized Likelihood Ratio Test

KW - Multichannel Coherence

KW - Multichannel Signal Detection

KW - Test for Block Independence

UR - http://www.scopus.com/inward/record.url?scp=84890468766&partnerID=8YFLogxK

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U2 - 10.1109/ICASSP.2013.6638393

DO - 10.1109/ICASSP.2013.6638393

M3 - Conference contribution

AN - SCOPUS:84890468766

SN - 9781479903566

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - 3919

EP - 3923

BT - 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings

T2 - 2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013

Y2 - 26 May 2013 through 31 May 2013

ER -