385 16.1 BIBO, Impulse Resprise arid Frequmcy Response Curve itrid calculate the value The result is only finite when thc inipulse response can be absolutely intcgrated, othcrwisc l g ( t ) I WOLIMriot Le I)onnckd As we discovered in Chapter 9.2.2, if the impulsc response can be abwluLely iritegratetl, the Fouricr transform H ( j w ) - F{h(t)}, the frequcricy response of the stable systerri rmist exi Because the Foiirier integral is 1)oiindrd (SCT (9.5)), d, arid is thv saim as thc L a p l a ~ etransform on the it c m be analytically corrti imaginary axis s = jw That mcaris that for slable systems, tlrp imagiiiarv axis of the s-plane is part of the rcgiori of c o i i v q p i c e of the system fuwtion '12-ic wnse of' a, stable system cannot h a w ariy siiigiilwrities or discontinuitirs ~ iscrete Systems For discrete LTI-systems: A discrete LTI-systcui is stable if and orily if its inipulsc response is I ~ (16.7) T h e prod is exactly as for continuou5 systems TL can be slion7ii in the same m7ay liom thci cxistenre ot thc frequel~c.yrcspot the Foiiricr translorrri I I ( d )= F*{h[kj}of tlie iinpiiBe response h [ k ]agrees m i t h the transfer function H ( z ) = Z { h [ k ] on } the iiiiit circlc of the :-planr Correspondingly, the fi cqucncy rtsporw o f R stnblc svstein m i s t riol h a w m y disc oritirriiities or ringularitics, JVe will clarifv the use of the stahilitv criterin (1 S.3) tor contiriuous systems with a k>wexsinplei Stdbility is showri in tlic s a n e way for discrete 5ybltims, using (16.7) Example 16.1 Fhr the simplest clxaniplc we consider a, system h ( t )= ~ - " ~ ; ( f ) with irqiilse rcspoiise rx E IR (16.8)