27SourceID - Energy Source Identification ) ( f H qy # 2 u...

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Unformatted text preview: Energy Source Identification ) ( f H qy # 2 u ) ( 1 f H y ) ( 2 f H y 1 v 2 v q v 1 u ) ( t n q u ) ( f H qq # ) ( 11 f H ) ( 22 f H 1 m 2 m q m 2 w 1 w q w ) ( 1 t x ) ( 2 t x ) ( t y ) ( t x q Measured Inputs Transducers Sources Input/Output System Measured Output Consider the multiple input-multiple output system with the transducer dynamics included as shown above. Here u are assumed to be the stationary sources with zero mean which are uncorrelated with the uncorrelated extraneous input and output noises with zero mean, and . Thus it holds q i t i , , 2 , 1 ), ( " = ) ( t n q i t m i , , 2 , 1 ), ( " = q j i G G G G G G j i j i i i i i i m w m m n v n w m w n m , , 2 , 1 , , " = = = = = = = . When sources are uncorrelated with each other and source measurements are free of noise, i.e. , and m , we can derive the ordinary coherence functions, using the relations and j i G j i u u ≠ = ; ) ( t y = ) ( = t i ) ( ) ( t n t + 1 v q i i ∑ = ) ( ) ( t w t x i i = , as 2 2 2 2 * 2 2 y u yy u u y u yy u u ii y u ii yy ii iy iy i i i i i i i G G G G G H G H G G G γ = = = = γ since it holds i i u u ii ii G H G 2 = , G . y u ii iy i G H * = Note here that the ordinary coherence functions between the source and output are well estimated using the measured input and output, independent of the transducer dynamics , as long as the dynamics are linear. The coherent output power spectrum is given by ii H vv q i yy iy q i v v x y G G G G i i ∑ ∑ = = = γ = = 1 2 1 : In general, x measured by any transducer, as long as its output is noise free and linearly related to the true source...
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This note was uploaded on 11/21/2009 for the course ME . taught by Professor . during the Spring '09 term at Korea University.

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27SourceID - Energy Source Identification ) ( f H qy # 2 u...

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