348 14 Discrete-Time LTI-Systems Figure 24.8: Forrning direct form I1 h r n direct form hem icylaced by tlir rvmplex vaxiable z We rim thcrclfolc also use mariy of the> techniques dwc4)pc.d for contiiiuous systems directly oil disc systems I’hi:, includes the relationships I-,etwec>nthe ~iff~rence/di~erenti a1 c on, block diagram arid state-space desciiptioiis (Chaptei 2.4), eqiiivalent state-space rc~prcscni ations (Chaptc.1 2.5) a i d controllability and observability (Chapter ) Figine 14.10 shows t Ire block tliagrarii of the st atc-space description for a discrete LTI-system with state qiations (14.26), (14.27), ancl (14.28), (14.29) Bc crtrefiil n o t to roiifuse tlic state vector in the timc-domain ~ [ kwibh ] the frequency variable of the z-t rallsfoKrn! In the case of initial condition problems de ibed by difference equat,ions, the state-space description (14.2G) and (11.27) can be extcnrled, tvlncre the system is offset to a suitable time ki, iri a suitable initial statcl ~[X-ojso that tl-it give11 initial coxidi t h i s ale fulfilled This can be achieved using a superiniposed impulse> zoSjk - ku], with which the statc.-space description is