25MISO1

# 25MISO1 - Multiple Input / Single Output Relationships...

This preview shows pages 1–3. Sign up to view the full content.

Multiple Input / Single Output Relationships Consider the multiple input-multiple output system shown below. Here are assumed to be the stationary inputs with zero mean which are uncorrelated with the uncorrelated extraneous output noise with zero mean, . Thus it holds q i t x i , , 2 , 1 ), ( " = ) ( t n q i f G n x i , , 2 , 1 , 0 ) ( " = = . ) ( τ q h # ) ( 2 t x ) ( 1 τ h ) ( 2 τ h ) ( 1 t v ) ( 2 t v ) ( t v q ) ( 1 t x ) ( t n ) ( t x q ) ( t y From the relation , we obtain the auto and cross-spectral densities as ) ( ) ( ) ( 1 t n t v t y q i i + = = nn q i q j x x j i nn q i q j v v yy G G H H G G G j i j i + = + = ∑∑ == 11 * = = = = = q i x x i q i v x y x q j G H G G i j i j j 1 1 , , 2 , 1 , " Similarly to the previous single input-single output relationship, we can obtain the optimal frequency response functions by minimizing the output noise power spectral density, which can be expressed as = = = = + = + = q i q j x x j i q i y x i q i yx i yy q i q j v v q i y v q i yv yy nn j i i i j i i i G H H G H G H G G G G G G * 1 * 1 1 1 Then, from 0 * = k nn H G , we derive the relation = = = q j kj j ky q k G H G 1 , , 2 , 1 , " or, in matrix form, = qy y y qq q q q q q G G G G G G G G G G G G H H H # " # # # " " # 2 1 1 2 1 2 22 21 1 12 11 2 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
MAE 591 RANDOM DATA Note that, for the optimal frequency response function, the output noise will automatically be uncorrelated with the inputs, since it holds . , , 2 , 1 , 0 q
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/21/2009 for the course ME . taught by Professor . during the Spring '09 term at Korea University.

### Page1 / 4

25MISO1 - Multiple Input / Single Output Relationships...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online