ECE634S09_L15_SystemRealization

ECE634S09_L15_SystemRealization - ECE634 Signals and...

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ECE634 Signals and Systems II, Spring 2009 - Lecture 15, February 25 Daniel S. Brogan 1 4.6 System Realization Recall the Time-Integration Property For ( ) ( ) x t X s , ( ) ( ) 0 t X s x d s τ τ Thus, Fig. 4.19 (Lathi) shows that an integrator block in the time domain becomes a 1/ s block in the complex frequency domain. Direct Form I Realization Using the complex-frequency domain definition of an integrator, we can rearrange any transfer function into a collection of scaled integrators. Below is an example for a third-order system. ( ) ( ) ( ) 1 2 3 1 2 3 2 0 2 3 0 1 2 3 3 1 2 0 3 2 2 3 3 3 1 2 1 2 1 2 3 2 3 2 3 1 1 1 H s H s b b b b b s b s b s b b b b s s s H s b a a a a a a s a s a s a s s s s s s s s s + + + + + + = = = + + + + + + + + + + + + ±²²²³²²²´ ±²²²³²²²´ ( ) ( ) ( ) ( ) ( ) 1 2 3 3 1 2 1 2 0 2 3 2 3 1/ 1 H s H s b a b b a a X s b W s Y s s s s s s s + + + = = + + + ±²²²³²²²´ ±²²²³²²²´ ( ) ( ) ( ) 3 1 2 2 3 a a a Y s W s Y s s s s = + +
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