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ECE634 Signals and Systems II, Spring 2009 - Lecture 15, February 25 Daniel S. Brogan 14.6 System Realization •Recall the Time-Integration Property For ( )( )x tXs⇔, ( )( )0tXsxdsττ−⇔∫Thus, Fig. 4.19 (Lathi) shows that an integrator block in the time domain becomes a 1/sblock 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. ( )( )( )12312320230123312032233312121232323111HsHsbbbbb sb sb sbbbbsssHsbaaaaaasa sa sasssssssss⎛⎞+++⎜⎟+++⎛⎞===+++⎜⎟⎜⎟+++⎝⎠⎜⎟++++++⎝⎠±²²²³²²²´±²²²³²²²´( )( )( )( )( )12331212023231/1HsHsbabbaaXsbWsYsssssss⎛⎞⎛⎞+++==+++⎜⎟⎜⎟⎝⎠⎝⎠±²²²³²²²´±²²²³²²²´( )( )( )31223aaaYsWsYssss⎛⎞=−++⎜⎟⎝⎠
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