. The analysis of multichannel two-dimensional random signals. CO • • • (a) 2-D data 1st prediction direction. K ■H 2nd prediction direction(b) Multichannel data Figure Multichannel 2-D linear prediction and related multichannel 1-D problem. 33 where each block a*, is of size M x M. The a[n) are found by solving the equation R olPx = R a i) a (Fi-l] 0 () where EPl is the P2M x P2M prediction error covariance and where the correlation matrixappearing on the left side of () is the same as that in (). Now post mulitply bothsides of Eq. () by the term A(0) and compare the resul

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. The analysis of multichannel two-dimensional random signals. CO • • • (a) 2-D data 1st prediction direction. K ■H 2nd prediction direction(b) Multichannel data Figure Multichannel 2-D linear prediction and related multichannel 1-D problem. 33 where each block a*, is of size M x M. The a[n) are found by solving the equation R olPx = R a i) a (Fi-l] 0 () where EPl is the P2M x P2M prediction error covariance and where the correlation matrixappearing on the left side of () is the same as that in (). Now post mulitply bothsides of Eq. () by the term A(0) and compare the result to Eq. (). In view of Eqs() and (), Eq. () will be identical to Eq. () if we require EFlA(0) =S(0) () and 0,1,. ..,Pi -1 () The foregoing equations show that the multichannel 2-D Normal equations can besolved by the following steps. First solve the P2M-dimensional 1-D multichannel problem(). Since this problem is 1-D, the multichannel Levinson recursion can be employedto find the coefficient matrices aSn^ and the prediction error covariance matrix EPl. Nextsolve ()

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