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HW_11(483)S09_Solns

HW_11(483)S09_Solns - EE 483 Digital Signal Processing...

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1 EE 483 – Digital Signal Processing Spring 2009 Homework #11 Solutions 11.1 Analysis yields w 1 [ n ] = β 1 α 1 w 2 [ n - 1] α 2 w 4 [ n - 1] α 3 w 6 [ n - 1] { } , w 2 [ n ] = w 1 [ n ] x [ n ], w 3 [ n ] = β 2 α 2 w 4 [ n - 1] α 3 w 6 [ n - 1] { } , w 4 [ n ] = w 2 [ n ] w 3 [ n ], w 5 [ n ] = β 3 α 3 w 6 [ n - 1] { } , w 6 [ n ] = w 4 [ n ] w 5 [ n ], y [ n ] = α 1 w 2 [ n ] α 2 w 4 [ n ] α 3 w 6 [ n ] α 0 x [ n ]. In matrix form the above set of equations are given by 1 1 1 1 1 2 2 2 3 3 4 4 5 5 6 6 1 2 3 0 0 0 0 0 0 0 [ ] [ ] 0 0 0 1 0 0 0 0 0 0 [ ] [ ] 0 0 0 0 0 0 0 [ ] [ ] 0 1 1 0 0 0 0 [ ] [ ] 0 0 0 0 0 0 0 [ ] [ ] 0 0 0 1 1 0 0 [ ] [ ] 0 0 0 0 [ ] [ ] w n w n w n w n w n w n w n w n w n w n w n w n a a a y n y n β α β α β = + 1 3 1 2 2 2 2 3 3 4 3 3 5 6 0 0 0 [ 1] [ ] 0 0 0 0 0 0 0 [ 1] 0 0 0 0 0 0 [ 1] 0 0 0 0 0 0 0 0 [ 1] 0 0 0 0 0 0 0 [ 1] 0 0 0 0 0 0 0 0 [ 1] [ ] 0 0 0 0 0 0 0 [ 1] w n x n w n w n w n w n w n x n y n α β α β α β α α -     -     -   + -     -   -  
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